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[Merged by Bors] - feat(model_theory/direct_limit): Direct limits of first-order structures #11789

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[Merged by Bors] - feat(model_theory/direct_limit): Direct limits of first-order structures #11789

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@awainverse awainverse commented Feb 3, 2022 •
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Constructs the direct limit of a directed system of first-order embeddings

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@awainverse awainverse added the awaiting-review The author would like community review of the PR label Feb 3, 2022
@awainverse awainverse added the blocked-by-other-PR This PR depends on another PR which is still in the queue. A bot manages this label via PR comment. label Feb 5, 2022
@leanprover-community-bot-assistant leanprover-community-bot-assistant removed the blocked-by-other-PR This PR depends on another PR which is still in the queue. A bot manages this label via PR comment. label Feb 7, 2022
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@leanprover-community-bot-assistant leanprover-community-bot-assistant added the merge-conflict Please `git merge origin/master` then a bot will remove this label. label Feb 7, 2022
@leanprover-community-bot-assistant leanprover-community-bot-assistant removed the merge-conflict Please `git merge origin/master` then a bot will remove this label. label Feb 7, 2022
fpvandoorn
fpvandoorn reviewed Feb 10, 2022
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LGTM, some minor comments

src/data/fintype/order.lean

lemma fintype.exists_le [nonempty α] [preorder α] [is_directed α (≤)]
{β : Type*} [fintype β] (f : β → α) :
∃ M, ∀ i, (f i) ≤ M :=
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This is usually written as bdd_above (range f) (but it's not definitionally equal)

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I think I'll add a bdd_above (range f) version of this, but I'll leave this one in analogy to https://leanprover-community.github.io/mathlib_docs/data/finset/order.html#finset.exists_le which is the lemma used by most of the algebra library for about this purpose.

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I will also briefly look into which version works better for my purposes later... if I'm unsure, I will push the version with bdd_above and upper_bounds and I can revert it if it's worse.

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I have now pushed a version in terms of bdd_above.

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@fpvandoorn fpvandoorn added awaiting-author A reviewer has asked the author a question or requested changes and removed awaiting-review The author would like community review of the PR labels Feb 10, 2022
@awainverse awainverse added awaiting-review The author would like community review of the PR and removed awaiting-author A reviewer has asked the author a question or requested changes labels Feb 10, 2022
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bors merge

@github-actions github-actions bot added ready-to-merge All that is left is for bors to build and merge this PR. (Remember you need to say `bors r+`.) and removed awaiting-review The author would like community review of the PR labels Feb 11, 2022
bors bot pushed a commit that referenced this pull request Feb 11, 2022
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feat(model_theory/direct_limit): Direct limits of first-order structu…
492393b 
…res (#11789)

Constructs the direct limit of a directed system of first-order embeddings
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bors bot commented Feb 11, 2022

Pull request successfully merged into master.

Build succeeded:

@bors bors bot changed the title feat(model_theory/direct_limit): Direct limits of first-order structures [Merged by Bors] - feat(model_theory/direct_limit): Direct limits of first-order structures Feb 11, 2022
@bors bors bot closed this Feb 11, 2022
@bors bors bot deleted the fo_direct_limit branch February 11, 2022 13:10
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