diff --git a/NEWS.md b/NEWS.md
index b941676ecf..39f73214e3 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -18,7 +18,8 @@ Breaking renames and type changes:
 - `Constraint.SOCRBridge` has been renamed to `Constraint.SOCtoRSOCBridge`
 - `RawParameter` has been renamed to `RawOptimizerAttribute` and now takes
   `String` instead of `Any` as the only argument
-- `Test.TestConfig` has been renamed to `Test.Config`
+- `Test.TestConfig` has been renamed to `Test.Config`    
+- `IndicatorSet` has been renamed to `Indicator`
 
 Breaking behavior changes:
 
diff --git a/docs/src/manual/constraints.md b/docs/src/manual/constraints.md
index b7a3df04e2..64bc478bda 100644
--- a/docs/src/manual/constraints.md
+++ b/docs/src/manual/constraints.md
@@ -172,7 +172,7 @@ where ``\mathcal{E}`` is the exponential cone (see [`ExponentialCone`](@ref)),
 | ``x_i \in \{0\} \cup \{l,l+1,\ldots,u-1,u\}``                                              | `SingleVariable`       | `Semiinteger`                      |
 | At most one component of ``x`` can be nonzero                                              | `VectorOfVariables`    | `SOS1`                             |
 | At most two components of ``x`` can be nonzero, and if so they must be adjacent components | `VectorOfVariables`    | `SOS2`                             |
-| ``y = 1 \implies a^T x \in S``                                                             | `VectorAffineFunction` | `IndicatorSet`                     |
+| ``y = 1 \implies a^T x \in S``                                                             | `VectorAffineFunction` | `Indicator`                        |
 
 ## JuMP mapping
 
diff --git a/docs/src/manual/standard_form.md b/docs/src/manual/standard_form.md
index e4600da18f..4a0fcc9343 100644
--- a/docs/src/manual/standard_form.md
+++ b/docs/src/manual/standard_form.md
@@ -149,7 +149,7 @@ or solver developers.
   A special ordered set of Type I.
 * [`SOS2(weights)`](@ref MathOptInterface.SOS2):
   A special ordered set of Type II.
-* [`IndicatorSet(set)`](@ref MathOptInterface.IndicatorSet):
+* [`Indicator(set)`](@ref MathOptInterface.Indicator):
   A set to specify indicator constraints.
 * [`Complements`](@ref MathOptInterface.Complements):
   A set for mixed complementarity constraints.
diff --git a/docs/src/reference/standard_form.md b/docs/src/reference/standard_form.md
index d3ad803b4f..c0b33bfad3 100644
--- a/docs/src/reference/standard_form.md
+++ b/docs/src/reference/standard_form.md
@@ -91,7 +91,7 @@ NormSpectralCone
 NormNuclearCone
 SOS1
 SOS2
-IndicatorSet
+Indicator
 Complements
 ```
 
diff --git a/src/Bridges/Constraint/indicator_activate_on_zero.jl b/src/Bridges/Constraint/indicator_activate_on_zero.jl
index f787e1f86b..44d3081bbb 100644
--- a/src/Bridges/Constraint/indicator_activate_on_zero.jl
+++ b/src/Bridges/Constraint/indicator_activate_on_zero.jl
@@ -21,7 +21,7 @@ struct IndicatorActiveOnFalseBridge{
     }
     indicator_cons_index::MOI.ConstraintIndex{
         F,
-        MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE,S},
+        MOI.Indicator{MOI.ACTIVATE_ON_ONE,S},
     }
 end
 
@@ -34,7 +34,7 @@ function bridge_constraint(
     S<:MOI.AbstractScalarSet,
     T<:Real,
     F,
-    IS<:MOI.IndicatorSet{MOI.ACTIVATE_ON_ZERO,S},
+    IS<:MOI.Indicator{MOI.ACTIVATE_ON_ZERO,S},
 }
     f_scalars = MOIU.eachscalar(f)
     z2, zo_cons = MOI.add_constrained_variable(model, MOI.ZeroOne())
@@ -42,18 +42,15 @@ function bridge_constraint(
     z1_z2 = MOIU.operate(+, T, f_scalars[1], MOI.SingleVariable(z2))
     dcons = MOIU.normalize_and_add_constraint(model, z1_z2, MOI.EqualTo(one(T)))
     f2 = MOIU.operate(vcat, T, MOI.SingleVariable(z2), f_scalars[2])
-    ci = MOI.add_constraint(
-        model,
-        f2,
-        MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(s.set),
-    )
+    ci =
+        MOI.add_constraint(model, f2, MOI.Indicator{MOI.ACTIVATE_ON_ONE}(s.set))
     return IndicatorActiveOnFalseBridge{T,F,S}(z2, zo_cons, dcons, ci)
 end
 
 function MOI.supports_constraint(
     ::Type{<:IndicatorActiveOnFalseBridge{T}},
     ::Type{<:MOI.VectorAffineFunction},
-    ::Type{<:MOI.IndicatorSet{MOI.ACTIVATE_ON_ZERO}},
+    ::Type{<:MOI.Indicator{MOI.ACTIVATE_ON_ZERO}},
 ) where {T}
     return true
 end
@@ -69,14 +66,14 @@ function MOIB.added_constraint_types(
 ) where {T,F,S}
     return [
         (MOI.ScalarAffineFunction{T}, MOI.EqualTo{T}),
-        (F, MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE,S}),
+        (F, MOI.Indicator{MOI.ACTIVATE_ON_ONE,S}),
     ]
 end
 
 function concrete_bridge_type(
     ::Type{<:IndicatorActiveOnFalseBridge{T}},
     ::Type{F},
-    ::Type{MOI.IndicatorSet{MOI.ACTIVATE_ON_ZERO,S}},
+    ::Type{MOI.Indicator{MOI.ACTIVATE_ON_ZERO,S}},
 ) where {T,F<:MOI.VectorAffineFunction,S<:MOI.AbstractScalarSet}
     return IndicatorActiveOnFalseBridge{T,F,S}
 end
@@ -84,7 +81,7 @@ end
 function concrete_bridge_type(
     ::Type{<:IndicatorActiveOnFalseBridge},
     ::Type{F},
-    ::Type{MOI.IndicatorSet{MOI.ACTIVATE_ON_ZERO,S}},
+    ::Type{MOI.Indicator{MOI.ACTIVATE_ON_ZERO,S}},
 ) where {F<:MOI.VectorAffineFunction,S<:MOI.AbstractScalarSet}
     return IndicatorActiveOnFalseBridge{Float64,F,S}
 end
diff --git a/src/Bridges/Constraint/indicator_sos.jl b/src/Bridges/Constraint/indicator_sos.jl
index 2f74789e7a..266263e821 100644
--- a/src/Bridges/Constraint/indicator_sos.jl
+++ b/src/Bridges/Constraint/indicator_sos.jl
@@ -30,7 +30,7 @@ function bridge_constraint(
     ::Type{IndicatorSOS1Bridge{T,BC,MaybeBC}},
     model::MOI.ModelLike,
     f::MOI.VectorAffineFunction{T},
-    s::MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE,BC},
+    s::MOI.Indicator{MOI.ACTIVATE_ON_ONE,BC},
 ) where {T<:Real,BC,MaybeBC}
     f_scalars = MOIU.eachscalar(f)
     (w, bound_constraint) = _add_bound_constraint!(model, BC)
@@ -68,7 +68,7 @@ end
 function MOI.supports_constraint(
     ::Type{<:IndicatorSOS1Bridge},
     ::Type{<:MOI.AbstractVectorFunction},
-    ::Type{<:MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE,<:MOI.AbstractScalarSet}},
+    ::Type{<:MOI.Indicator{MOI.ACTIVATE_ON_ONE,<:MOI.AbstractScalarSet}},
 )
     return true
 end
@@ -78,7 +78,7 @@ function MOI.get(
     attr::MOI.ConstraintSet,
     b::IndicatorSOS1Bridge,
 )
-    return MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(
+    return MOI.Indicator{MOI.ACTIVATE_ON_ONE}(
         MOI.get(model, attr, b.linear_constraint_index),
     )
 end
@@ -139,7 +139,7 @@ end
 function concrete_bridge_type(
     ::Type{<:IndicatorSOS1Bridge{T}},
     ::Type{<:MOI.AbstractVectorFunction},
-    ::Type{MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE,S}},
+    ::Type{MOI.Indicator{MOI.ACTIVATE_ON_ONE,S}},
 ) where {T,S<:Union{MOI.LessThan,MOI.GreaterThan}}
     return IndicatorSOS1Bridge{T,S,MOI.ConstraintIndex{MOI.SingleVariable,S}}
 end
@@ -147,7 +147,7 @@ end
 function concrete_bridge_type(
     ::Type{<:IndicatorSOS1Bridge{T}},
     ::Type{<:MOI.AbstractVectorFunction},
-    ::Type{MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE,S}},
+    ::Type{MOI.Indicator{MOI.ACTIVATE_ON_ONE,S}},
 ) where {T,S<:MOI.AbstractScalarSet}
     return IndicatorSOS1Bridge{T,S,Nothing}
 end
diff --git a/src/DeprecatedTest/UnitTests/basic_constraint_tests.jl b/src/DeprecatedTest/UnitTests/basic_constraint_tests.jl
index eebe5d891a..bc3422e7da 100644
--- a/src/DeprecatedTest/UnitTests/basic_constraint_tests.jl
+++ b/src/DeprecatedTest/UnitTests/basic_constraint_tests.jl
@@ -143,19 +143,19 @@ const BasicConstraintTests = Dict(
     (MOI.VectorAffineFunction{Float64}, MOI.PositiveSemidefiniteConeSquare) => (dummy_vector_affine, 9, MOI.PositiveSemidefiniteConeSquare(3)),
     (
         MOI.VectorAffineFunction{Float64},
-        MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE,MOI.LessThan{Float64}},
+        MOI.Indicator{MOI.ACTIVATE_ON_ONE,MOI.LessThan{Float64}},
     ) => (
         dummy_vector_affine,
         2,
-        MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(3.0)),
+        MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(3.0)),
     ),
     (
         MOI.VectorAffineFunction{Float64},
-        MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE,MOI.GreaterThan{Float64}},
+        MOI.Indicator{MOI.ACTIVATE_ON_ONE,MOI.GreaterThan{Float64}},
     ) => (
         dummy_vector_affine,
         2,
-        MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.GreaterThan(3.0)),
+        MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.GreaterThan(3.0)),
     ),
     (MOI.VectorQuadraticFunction{Float64}, MOI.Zeros) =>
         (dummy_vector_quadratic, 2, MOI.Zeros(2)),
diff --git a/src/DeprecatedTest/intlinear.jl b/src/DeprecatedTest/intlinear.jl
index 852ae5e7a9..be9d998617 100644
--- a/src/DeprecatedTest/intlinear.jl
+++ b/src/DeprecatedTest/intlinear.jl
@@ -551,7 +551,7 @@ function indicator1_test(model::MOI.ModelLike, config::Config)
     @test MOI.supports_constraint(
         model,
         MOI.VectorAffineFunction{Float64},
-        MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE,MOI.LessThan{Float64}},
+        MOI.Indicator{MOI.ACTIVATE_ON_ONE,MOI.LessThan{Float64}},
     )
     x1 = MOI.add_variable(model)
     x2 = MOI.add_variable(model)
@@ -566,7 +566,7 @@ function indicator1_test(model::MOI.ModelLike, config::Config)
         ],
         [0.0, 0.0],
     )
-    iset1 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(8.0))
+    iset1 = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(8.0))
     MOI.add_constraint(model, f1, iset1)
     f2 = MOI.VectorAffineFunction(
         [
@@ -576,7 +576,7 @@ function indicator1_test(model::MOI.ModelLike, config::Config)
         ],
         [0.0, 0.0],
     )
-    iset2 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(9.0))
+    iset2 = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(9.0))
     MOI.add_constraint(model, f2, iset2)
     # Additional regular constraint.
     MOI.add_constraint(
@@ -648,7 +648,7 @@ function indicator2_test(model::MOI.ModelLike, config::Config)
         ],
         [0.0, 0.0],
     )
-    iset1 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(8.0))
+    iset1 = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(8.0))
     MOI.add_constraint(model, f1, iset1)
     f2 = MOI.VectorAffineFunction(
         [
@@ -658,7 +658,7 @@ function indicator2_test(model::MOI.ModelLike, config::Config)
         ],
         [0.0, 0.0],
     )
-    iset2 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(9.0))
+    iset2 = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(9.0))
     MOI.add_constraint(model, f2, iset2)
     # additional regular constraint
     MOI.add_constraint(
@@ -737,7 +737,7 @@ function indicator3_test(model::MOI.ModelLike, config::Config)
     @test MOI.supports_constraint(
         model,
         MOI.VectorAffineFunction{Float64},
-        MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE,MOI.LessThan{Float64}},
+        MOI.Indicator{MOI.ACTIVATE_ON_ONE,MOI.LessThan{Float64}},
     )
     x1 = MOI.add_variable(model)
     x2 = MOI.add_variable(model)
@@ -754,7 +754,7 @@ function indicator3_test(model::MOI.ModelLike, config::Config)
         ],
         [0.0, 0.0],
     )
-    iset1 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ZERO}(MOI.LessThan(8.0))
+    iset1 = MOI.Indicator{MOI.ACTIVATE_ON_ZERO}(MOI.LessThan(8.0))
     MOI.add_constraint(model, f1, iset1)
     f2 = MOI.VectorAffineFunction(
         [
@@ -764,7 +764,7 @@ function indicator3_test(model::MOI.ModelLike, config::Config)
         ],
         [0.0, 0.0],
     )
-    iset2 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(9.0))
+    iset2 = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(9.0))
     MOI.add_constraint(model, f2, iset2)
     # Additional regular constraint.
     MOI.add_constraint(
@@ -842,7 +842,7 @@ function indicator4_test(model::MOI.ModelLike, config::Config)
     @test MOI.supports_constraint(
         model,
         MOI.VectorAffineFunction{Float64},
-        MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE,MOI.LessThan{Float64}},
+        MOI.Indicator{MOI.ACTIVATE_ON_ONE,MOI.LessThan{Float64}},
     )
     x1 = MOI.add_variable(model)
     x2 = MOI.add_variable(model)
@@ -857,7 +857,7 @@ function indicator4_test(model::MOI.ModelLike, config::Config)
         ],
         [0.0, -1.0],
     )
-    iset1 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(7.0))
+    iset1 = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(7.0))
     MOI.add_constraint(model, f1, iset1)
     f2 = MOI.VectorAffineFunction(
         [
@@ -867,7 +867,7 @@ function indicator4_test(model::MOI.ModelLike, config::Config)
         ],
         [0.0, 1.0],
     )
-    iset2 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(10.0))
+    iset2 = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(10.0))
     MOI.add_constraint(model, f2, iset2)
     # Additional regular constraint.
     MOI.add_constraint(
diff --git a/src/FileFormats/MOF/MOF.jl b/src/FileFormats/MOF/MOF.jl
index 6aa24518ac..a42c86dd04 100644
--- a/src/FileFormats/MOF/MOF.jl
+++ b/src/FileFormats/MOF/MOF.jl
@@ -64,7 +64,7 @@ MOI.Utilities.@model(
     (MOI.VectorAffineFunction, MOI.VectorQuadraticFunction)
 )
 
-# IndicatorSet is handled by UniversalFallback.
+# Indicator is handled by UniversalFallback.
 
 const Model = MOI.Utilities.UniversalFallback{InnerModel{Float64}}
 
diff --git a/src/FileFormats/MOF/read.jl b/src/FileFormats/MOF/read.jl
index 15f9bbafb9..ee4b15f0af 100644
--- a/src/FileFormats/MOF/read.jl
+++ b/src/FileFormats/MOF/read.jl
@@ -477,5 +477,5 @@ function set_to_moi(::Val{:IndicatorSet}, object::Object)
         @assert object["activate_on"]::String == "zero"
         MOI.ACTIVATE_ON_ZERO
     end
-    return MOI.IndicatorSet{indicator}(set)
+    return MOI.Indicator{indicator}(set)
 end
diff --git a/src/FileFormats/MOF/write.jl b/src/FileFormats/MOF/write.jl
index 675eb3f3c8..05c971a67e 100644
--- a/src/FileFormats/MOF/write.jl
+++ b/src/FileFormats/MOF/write.jl
@@ -295,7 +295,7 @@ head_name(::Type{<:MOI.SOS1}) = "SOS1"
 head_name(::Type{<:MOI.SOS2}) = "SOS2"
 
 function moi_to_object(
-    set::MOI.IndicatorSet{I,S},
+    set::MOI.Indicator{I,S},
     name_map::Dict{MOI.VariableIndex,String},
 ) where {I,S}
     @assert I == MOI.ACTIVATE_ON_ONE || I == MOI.ACTIVATE_ON_ZERO
diff --git a/src/Test/test_basic_constraint.jl b/src/Test/test_basic_constraint.jl
index 494a22a3bc..e37c4c4d5b 100644
--- a/src/Test/test_basic_constraint.jl
+++ b/src/Test/test_basic_constraint.jl
@@ -104,16 +104,14 @@ _set(::Type{MOI.RootDetConeTriangle}) = MOI.RootDetConeTriangle(3)
 _set(::Type{MOI.RootDetConeSquare}) = MOI.RootDetConeSquare(3)
 _set(::Type{MOI.Complements}) = MOI.Complements(2)
 
-function _set(
-    ::Type{MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE,MOI.LessThan{Float64}}},
-)
-    return MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(3.0))
+function _set(::Type{MOI.Indicator{MOI.ACTIVATE_ON_ONE,MOI.LessThan{Float64}}})
+    return MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(3.0))
 end
 
 function _set(
-    ::Type{MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE,MOI.GreaterThan{Float64}}},
+    ::Type{MOI.Indicator{MOI.ACTIVATE_ON_ONE,MOI.GreaterThan{Float64}}},
 )
-    return MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.GreaterThan(3.0))
+    return MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.GreaterThan(3.0))
 end
 
 function _basic_constraint_test_helper(
@@ -281,7 +279,7 @@ function test_basic_VectorAffineFunction_Indicator_LessThan(
         model,
         config,
         MOI.VectorAffineFunction,
-        MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE,MOI.LessThan{Float64}},
+        MOI.Indicator{MOI.ACTIVATE_ON_ONE,MOI.LessThan{Float64}},
     )
     return
 end
@@ -294,7 +292,7 @@ function test_basic_VectorAffineFunction_Indicator_GreaterThan(
         model,
         config,
         MOI.VectorAffineFunction,
-        MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE,MOI.GreaterThan{Float64}},
+        MOI.Indicator{MOI.ACTIVATE_ON_ONE,MOI.GreaterThan{Float64}},
     )
     return
 end
diff --git a/src/Test/test_linear.jl b/src/Test/test_linear.jl
index 045ab03889..f71ea70f27 100644
--- a/src/Test/test_linear.jl
+++ b/src/Test/test_linear.jl
@@ -3497,7 +3497,7 @@ function test_linear_Indicator_integration(model::MOI.ModelLike, config::Config)
     @requires MOI.supports_constraint(
         model,
         MOI.VectorAffineFunction{Float64},
-        MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE,MOI.LessThan{Float64}},
+        MOI.Indicator{MOI.ACTIVATE_ON_ONE,MOI.LessThan{Float64}},
     )
     x1 = MOI.add_variable(model)
     x2 = MOI.add_variable(model)
@@ -3512,7 +3512,7 @@ function test_linear_Indicator_integration(model::MOI.ModelLike, config::Config)
         ],
         [0.0, 0.0],
     )
-    iset1 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(8.0))
+    iset1 = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(8.0))
     MOI.add_constraint(model, f1, iset1)
     f2 = MOI.VectorAffineFunction(
         [
@@ -3522,7 +3522,7 @@ function test_linear_Indicator_integration(model::MOI.ModelLike, config::Config)
         ],
         [0.0, 0.0],
     )
-    iset2 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(9.0))
+    iset2 = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(9.0))
     MOI.add_constraint(model, f2, iset2)
     # Additional regular constraint.
     MOI.add_constraint(
@@ -3604,7 +3604,7 @@ function test_linear_Indicator_ON_ONE(model::MOI.ModelLike, config::Config)
         ],
         [0.0, 0.0],
     )
-    iset1 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(8.0))
+    iset1 = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(8.0))
     MOI.add_constraint(model, f1, iset1)
     f2 = MOI.VectorAffineFunction(
         [
@@ -3614,7 +3614,7 @@ function test_linear_Indicator_ON_ONE(model::MOI.ModelLike, config::Config)
         ],
         [0.0, 0.0],
     )
-    iset2 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(9.0))
+    iset2 = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(9.0))
     MOI.add_constraint(model, f2, iset2)
     # additional regular constraint
     MOI.add_constraint(
@@ -3703,7 +3703,7 @@ function test_linear_Indicator_ON_ZERO(model::MOI.ModelLike, config::Config)
     @requires MOI.supports_constraint(
         model,
         MOI.VectorAffineFunction{Float64},
-        MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE,MOI.LessThan{Float64}},
+        MOI.Indicator{MOI.ACTIVATE_ON_ONE,MOI.LessThan{Float64}},
     )
     x1 = MOI.add_variable(model)
     x2 = MOI.add_variable(model)
@@ -3720,7 +3720,7 @@ function test_linear_Indicator_ON_ZERO(model::MOI.ModelLike, config::Config)
         ],
         [0.0, 0.0],
     )
-    iset1 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ZERO}(MOI.LessThan(8.0))
+    iset1 = MOI.Indicator{MOI.ACTIVATE_ON_ZERO}(MOI.LessThan(8.0))
     MOI.add_constraint(model, f1, iset1)
     f2 = MOI.VectorAffineFunction(
         [
@@ -3730,7 +3730,7 @@ function test_linear_Indicator_ON_ZERO(model::MOI.ModelLike, config::Config)
         ],
         [0.0, 0.0],
     )
-    iset2 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(9.0))
+    iset2 = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(9.0))
     MOI.add_constraint(model, f2, iset2)
     # Additional regular constraint.
     MOI.add_constraint(
@@ -3822,7 +3822,7 @@ function test_linear_Indicator_constant_term(
     @requires MOI.supports_constraint(
         model,
         MOI.VectorAffineFunction{Float64},
-        MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE,MOI.LessThan{Float64}},
+        MOI.Indicator{MOI.ACTIVATE_ON_ONE,MOI.LessThan{Float64}},
     )
     x1 = MOI.add_variable(model)
     x2 = MOI.add_variable(model)
@@ -3837,7 +3837,7 @@ function test_linear_Indicator_constant_term(
         ],
         [0.0, -1.0],
     )
-    iset1 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(7.0))
+    iset1 = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(7.0))
     MOI.add_constraint(model, f1, iset1)
     f2 = MOI.VectorAffineFunction(
         [
@@ -3847,7 +3847,7 @@ function test_linear_Indicator_constant_term(
         ],
         [0.0, 1.0],
     )
-    iset2 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(10.0))
+    iset2 = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(10.0))
     MOI.add_constraint(model, f2, iset2)
     # Additional regular constraint.
     MOI.add_constraint(
diff --git a/src/Utilities/model.jl b/src/Utilities/model.jl
index bb7d389217..4abfb856de 100644
--- a/src/Utilities/model.jl
+++ b/src/Utilities/model.jl
@@ -886,10 +886,10 @@ for (loop_name, loop_super_type) in [
     end
 end
 
-const LessThanIndicatorSetOne{T} =
-    MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE,MOI.LessThan{T}}
-const LessThanIndicatorSetZero{T} =
-    MOI.IndicatorSet{MOI.ACTIVATE_ON_ZERO,MOI.LessThan{T}}
+const LessThanIndicatorOne{T} =
+    MOI.Indicator{MOI.ACTIVATE_ON_ONE,MOI.LessThan{T}}
+const LessThanIndicatorZero{T} =
+    MOI.Indicator{MOI.ACTIVATE_ON_ZERO,MOI.LessThan{T}}
 
 @model(
     Model,
@@ -930,8 +930,8 @@ const LessThanIndicatorSetZero{T} =
         MOI.DualPowerCone,
         MOI.SOS1,
         MOI.SOS2,
-        LessThanIndicatorSetOne,
-        LessThanIndicatorSetZero,
+        LessThanIndicatorOne,
+        LessThanIndicatorZero,
     ),
     (),
     (MOI.ScalarAffineFunction, MOI.ScalarQuadraticFunction),
diff --git a/src/sets.jl b/src/sets.jl
index f94a94c13e..9485006643 100644
--- a/src/sets.jl
+++ b/src/sets.jl
@@ -986,7 +986,7 @@ dimension(s::Union{SOS1,SOS2}) = length(s.weights)
 	ActivationCondition
 
 Activation condition for an indicator constraint.
-The enum value is used as first type parameter of `IndicatorSet{A,S}`.
+The enum value is used as first type parameter of `Indicator{A,S}`.
 """
 @enum ActivationCondition begin
     ACTIVATE_ON_ZERO
@@ -994,7 +994,7 @@ The enum value is used as first type parameter of `IndicatorSet{A,S}`.
 end
 
 """
-    IndicatorSet{A, S <: AbstractScalarSet}(set::S)
+    Indicator{A, S <: AbstractScalarSet}(set::S)
 
 ``\\{(y, x) \\in \\{0, 1\\} \\times \\mathbb{R}^n : y = 0 \\implies x \\in set\\}``
 when `A` is `ACTIVATE_ON_ZERO` and
@@ -1003,7 +1003,7 @@ when `A` is `ACTIVATE_ON_ONE`.
 
 `S` has to be a sub-type of `AbstractScalarSet`.
 `A` is one of the value of the `ActivationCond` enum.
-`IndicatorSet` is used with a `VectorAffineFunction` holding
+`Indicator` is used with a `VectorAffineFunction` holding
 the indicator variable first.
 
 Example: ``\\{(y, x) \\in \\{0, 1\\} \\times \\mathbb{R}^2 : y = 1 \\implies x_1 + x_2 \\leq 9 \\} ``
@@ -1017,26 +1017,23 @@ f = MOI.VectorAffineFunction(
     [0.0, 0.0],
 )
 
-indicator_set = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(9.0))
+indicator_set = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(9.0))
 
 MOI.add_constraint(model, f, indicator_set)
 ```
 """
-struct IndicatorSet{A,S<:AbstractScalarSet} <: AbstractVectorSet
+struct Indicator{A,S<:AbstractScalarSet} <: AbstractVectorSet
     set::S
-    IndicatorSet{A}(set::S) where {A,S<:AbstractScalarSet} = new{A,S}(set)
+    Indicator{A}(set::S) where {A,S<:AbstractScalarSet} = new{A,S}(set)
 end
 
-dimension(::IndicatorSet) = 2
+dimension(::Indicator) = 2
 
-function Base.copy(set::IndicatorSet{A,S}) where {A,S}
-    return IndicatorSet{A}(copy(set.set))
+function Base.copy(set::Indicator{A,S}) where {A,S}
+    return Indicator{A}(copy(set.set))
 end
 
-function Base.:(==)(
-    set1::IndicatorSet{A,S},
-    set2::IndicatorSet{A,S},
-) where {A,S}
+function Base.:(==)(set1::Indicator{A,S}, set2::Indicator{A,S}) where {A,S}
     return set1.set == set2.set
 end
 
diff --git a/test/Bridges/Constraint/indicator_activate_on_zero.jl b/test/Bridges/Constraint/indicator_activate_on_zero.jl
index 82e8954d17..d61175b825 100644
--- a/test/Bridges/Constraint/indicator_activate_on_zero.jl
+++ b/test/Bridges/Constraint/indicator_activate_on_zero.jl
@@ -48,7 +48,7 @@ function test_indicator_activate_on_zero()
         ],
         [0.0, 0.0],
     )
-    iset1 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ZERO}(MOI.LessThan(8.0))
+    iset1 = MOI.Indicator{MOI.ACTIVATE_ON_ZERO}(MOI.LessThan(8.0))
     BT = MOI.Bridges.Constraint.concrete_bridge_type(
         MOI.Bridges.Constraint.IndicatorActiveOnFalseBridge{Float64},
         typeof(f1),
diff --git a/test/Bridges/Constraint/indicator_sos.jl b/test/Bridges/Constraint/indicator_sos.jl
index c87294dfd9..1495a0e497 100644
--- a/test/Bridges/Constraint/indicator_sos.jl
+++ b/test/Bridges/Constraint/indicator_sos.jl
@@ -43,7 +43,7 @@ function test_indicator_by_SOS1()
         ],
         [0.0, 0.0],
     )
-    iset1 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(8.0))
+    iset1 = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(8.0))
 
     f2 = MOI.VectorAffineFunction(
         [
@@ -53,7 +53,7 @@ function test_indicator_by_SOS1()
         ],
         [0.0, 0.0],
     )
-    iset2 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.EqualTo(9.0))
+    iset2 = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.EqualTo(9.0))
 
     f3 = MOI.VectorAffineFunction(
         [
@@ -62,7 +62,7 @@ function test_indicator_by_SOS1()
         ],
         [0.0, 0.0],
     )
-    iset3 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.GreaterThan(5.0))
+    iset3 = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.GreaterThan(5.0))
 
     BT1 = MOI.Bridges.Constraint.concrete_bridge_type(
         MOI.Bridges.Constraint.IndicatorSOS1Bridge{Float64},
@@ -217,7 +217,7 @@ function test_model_equality()
         ],
         [0.0, 0.0],
     )
-    iset = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(8.0))
+    iset = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(8.0))
     ci = MOI.add_constraint(bridged_mock, f, iset)
     @test length(MOI.get(mock, MOI.ListOfVariableIndices())) == 3
     MOI.set(
@@ -315,7 +315,7 @@ function test_getting_primal_attributes()
         ],
         [0.0, 0.0],
     )
-    iset = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(8.0))
+    iset = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(8.0))
     BT = MOI.Bridges.Constraint.concrete_bridge_type(
         MOI.Bridges.Constraint.IndicatorSOS1Bridge{Float64},
         typeof(f),
@@ -341,7 +341,7 @@ function test_getting_primal_attributes()
         MOI.get(mock, MOI.ConstraintPrimalStart(), bridge1) .≈
         (1.0, affine_value - w_value),
     )
-    iseteq = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.EqualTo(8.0))
+    iseteq = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.EqualTo(8.0))
     BT = MOI.Bridges.Constraint.concrete_bridge_type(
         MOI.Bridges.Constraint.IndicatorSOS1Bridge{Float64},
         typeof(f),
diff --git a/test/Bridges/lazy_bridge_optimizer.jl b/test/Bridges/lazy_bridge_optimizer.jl
index cf12e89532..e46ef84c57 100644
--- a/test/Bridges/lazy_bridge_optimizer.jl
+++ b/test/Bridges/lazy_bridge_optimizer.jl
@@ -1535,8 +1535,8 @@ function MOI.Bridges.Constraint.concrete_bridge_type(
     return BridgeAddingNoConstraint{T}
 end
 
-const LessThanIndicatorSetOne{T} =
-    MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE,MOI.LessThan{T}}
+const LessThanIndicatorOne{T} =
+    MOI.Indicator{MOI.ACTIVATE_ON_ONE,MOI.LessThan{T}}
 
 MOI.Utilities.@model(
     ModelNoZeroIndicator,
@@ -1576,7 +1576,7 @@ MOI.Utilities.@model(
         MOI.DualPowerCone,
         MOI.SOS1,
         MOI.SOS2,
-        LessThanIndicatorSetOne,
+        LessThanIndicatorOne,
     ),
     (),
     (MOI.ScalarAffineFunction, MOI.ScalarQuadraticFunction),
@@ -1865,12 +1865,12 @@ function test_supports()
     @test !MOI.supports_constraint(
         mock_indicator,
         MOI.VectorAffineFunction{Float64},
-        MOI.IndicatorSet{MOI.ACTIVATE_ON_ZERO,MOI.LessThan{Float64}},
+        MOI.Indicator{MOI.ACTIVATE_ON_ZERO,MOI.LessThan{Float64}},
     )
     @test MOI.supports_constraint(
         full_bridged_mock_indicator,
         MOI.VectorAffineFunction{Float64},
-        MOI.IndicatorSet{MOI.ACTIVATE_ON_ZERO,MOI.LessThan{Float64}},
+        MOI.Indicator{MOI.ACTIVATE_ON_ZERO,MOI.LessThan{Float64}},
     )
 
     mock_sos_indicator =
@@ -1880,22 +1880,22 @@ function test_supports()
     @test !MOI.supports_constraint(
         mock_sos_indicator,
         MOI.VectorAffineFunction{Float64},
-        MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE,MOI.LessThan{Float64}},
+        MOI.Indicator{MOI.ACTIVATE_ON_ONE,MOI.LessThan{Float64}},
     )
     @test !MOI.supports_constraint(
         mock_sos_indicator,
         MOI.VectorAffineFunction{Float64},
-        MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE,MOI.EqualTo{Float64}},
+        MOI.Indicator{MOI.ACTIVATE_ON_ONE,MOI.EqualTo{Float64}},
     )
     @test MOI.supports_constraint(
         full_bridged_mock_sos_indicator,
         MOI.VectorAffineFunction{Float64},
-        MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE,MOI.LessThan{Float64}},
+        MOI.Indicator{MOI.ACTIVATE_ON_ONE,MOI.LessThan{Float64}},
     )
     @test MOI.supports_constraint(
         full_bridged_mock_sos_indicator,
         MOI.VectorAffineFunction{Float64},
-        MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE,MOI.EqualTo{Float64}},
+        MOI.Indicator{MOI.ACTIVATE_ON_ONE,MOI.EqualTo{Float64}},
     )
     for T in [Float64, Int]
         no_variable_mock = MOI.Utilities.MockOptimizer(NoVariableModel{T}())
diff --git a/test/FileFormats/MOF/MOF.jl b/test/FileFormats/MOF/MOF.jl
index 13142ca2a0..9d8e5f4718 100644
--- a/test/FileFormats/MOF/MOF.jl
+++ b/test/FileFormats/MOF/MOF.jl
@@ -763,12 +763,12 @@ c1: [t, x1, x2, x3, x4] in RootDetConeSquare(2)
     )
 end
 
-function test_IndicatorSet()
+function test_Indicator()
     _test_model_equality(
         """
 variables: x, y
 minobjective: x
-c1: [x, y] in IndicatorSet{ACTIVATE_ON_ONE}(GreaterThan(1.0))
+c1: [x, y] in Indicator{ACTIVATE_ON_ONE}(GreaterThan(1.0))
 """,
         ["x", "y"],
         ["c1"],
@@ -778,7 +778,7 @@ c1: [x, y] in IndicatorSet{ACTIVATE_ON_ONE}(GreaterThan(1.0))
         """
 variables: x, y
 minobjective: x
-c1: [x, y] in IndicatorSet{ACTIVATE_ON_ZERO}(GreaterThan(1.0))
+c1: [x, y] in Indicator{ACTIVATE_ON_ZERO}(GreaterThan(1.0))
 """,
         ["x", "y"],
         ["c1"],
diff --git a/test/sets.jl b/test/sets.jl
index 7f8fcab254..b2c5a16ca2 100644
--- a/test/sets.jl
+++ b/test/sets.jl
@@ -46,7 +46,7 @@ function test_sets_equals()
         @test S(a(), a()) != S(b(), b())
         @test S(a(), a()) == S(a(), a())
     end
-    S = MOI.IndicatorSet
+    S = MOI.Indicator
     A() = MOI.LessThan(a())
     B() = MOI.LessThan(b())
     @test S{MOI.ACTIVATE_ON_ZERO}(A()) == S{MOI.ACTIVATE_ON_ZERO}(A())
@@ -70,15 +70,15 @@ function test_sets_sos2_copy()
 end
 
 function test_sets_indicator_copy()
-    s1 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(4.0))
-    s2 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ZERO}(MOI.GreaterThan(4.0))
+    s1 = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(4.0))
+    s2 = MOI.Indicator{MOI.ACTIVATE_ON_ZERO}(MOI.GreaterThan(4.0))
     s1_copy = copy(s1)
     s2_copy = copy(s2)
-    @test s1_copy isa MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}
+    @test s1_copy isa MOI.Indicator{MOI.ACTIVATE_ON_ONE}
     @test s1 == s1_copy
-    @test s2_copy isa MOI.IndicatorSet{MOI.ACTIVATE_ON_ZERO}
+    @test s2_copy isa MOI.Indicator{MOI.ACTIVATE_ON_ZERO}
     @test s2 == s2_copy
-    s3 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ZERO}(MutLessThan(4.0))
+    s3 = MOI.Indicator{MOI.ACTIVATE_ON_ZERO}(MutLessThan(4.0))
     s3_copy = copy(s3)
     @test s3.set.upper ≈ 4.0
     s3_copy.set.upper = 5.0
@@ -109,7 +109,7 @@ function test_sets_dimension()
     @test MOI.dimension(MOI.SOS1([1.0, 2.0])) == 2
     @test MOI.dimension(MOI.SOS2([1.0, 2.0])) == 2
     @test MOI.dimension(
-        MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(1.0)),
+        MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(1.0)),
     ) == 2
     @test MOI.dimension(MOI.Complements(10)) == 10
 end