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references.bib
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references.bib
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# To normalize:
# bibtool --preserve.key.case=on --preserve.keys=on --pass.comments=on --print.use.tab=off -s -i docs/references.bib -o docs/references.bib
# https://www.zbmath.org/ and https://mathscinet.ams.org/mathscinet
# (or the free tool https://mathscinet.ams.org/mrlookup)
# are good sources of complete bibtex entries for mathematics
# To link to an entry in `references.bib`, use the following formats:
# [Author, *Title* (optional location)][bibkey]
@InProceedings{ adhesive2004,
author = {S. Lack and P. Soboci{\'n}ski},
title = {Adhesive categories},
booktitle = {Foundations of Software Science and Computation
Structures, {FoSSaCS '04}},
series = {LNCS},
volume = {2987},
pages = {273--288},
publisher = {Springer},
year = {2004},
url = {https://www.ioc.ee/~pawel/papers/adhesive.pdf}
}
@Article{ ahrens2017,
author = {Benedikt Ahrens and Peter LeFanu Lumsdaine},
year = {2019},
title = {Displayed Categories},
journal = {Logical Methods in Computer Science},
volume = {15},
issue = {1},
doi = {10.23638/LMCS-15(1:20)2019}
}
@Article{ aigner1999proofs,
author = {Aigner, Martin and Ziegler, G{\"u}nter M},
title = {Proofs from THE BOOK},
journal = {Berlin. Germany},
year = {1999},
publisher = {Springer}
}
@Article{ alfseneffros1972,
author = {Erik M. {Alfsen} and Edward G. {Effros}},
title = {{Structure in real Banach spaces. I and II}},
fjournal = {{Annals of Mathematics. Second Series}},
journal = {{Ann. Math. (2)}},
issn = {0003-486X},
volume = {96},
pages = {98--173},
year = {1972},
publisher = {Princeton University, Mathematics Department, Princeton,
NJ},
language = {English},
doi = {10.2307/1970895},
msc2010 = {46L05 46B10 46K05 46E15 46B99 46A40},
zbl = {0248.46019}
}
@Book{ alfsenshultz2003,
author = {Erik M. {Alfsen} and Frederic W. {Shultz}},
title = {{Geometry of state spaces of operator algebras}},
isbn = {0-8176-4319-2},
pages = {xiii + 467},
year = {2003},
publisher = {Boston, MA: Birkh\"auser},
language = {English},
msc2010 = {46-02 46L05 46L10 46L70 46L30 17C65},
zbl = {1042.46001}
}
@Book{ aluffi2016,
title = {Algebra: Chapter 0},
author = {Aluffi, Paolo},
series = {Graduate Studies in Mathematics},
volume = {104},
year = {2016},
publisher = {American Mathematical Society},
edition = {Reprinted with corrections by the American Mathematical
Society}
}
@Book{ atiyah-macdonald,
author = {Atiyah, M. F. and Macdonald, I. G.},
title = {Introduction to commutative algebra},
publisher = {Addison-Wesley Publishing Co., Reading, Mass.-London-Don
Mills, Ont.},
year = {1969},
pages = {ix+128},
mrclass = {13.00},
mrnumber = {0242802},
mrreviewer = {J. A. Johnson}
}
@InProceedings{ avigad-carneiro-hudon2019,
author = {Jeremy Avigad and Mario M. Carneiro and Simon Hudon},
editor = {John Harrison and John O'Leary and Andrew Tolmach},
title = {Data Types as Quotients of Polynomial Functors},
booktitle = {10th International Conference on Interactive Theorem
Proving, {ITP} 2019, September 9-12, 2019, Portland, OR,
{USA}},
series = {LIPIcs},
volume = {141},
pages = {6:1--6:19},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum f{\"{u}}r Informatik},
year = {2019},
url = {https://doi.org/10.4230/LIPIcs.ITP.2019.6},
doi = {10.4230/LIPIcs.ITP.2019.6},
timestamp = {Fri, 27 Sep 2019 15:57:06 +0200},
biburl = {https://dblp.org/rec/conf/itp/AvigadCH19.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@Misc{ avigad_moura_kong-2017,
author = {Jeremy Avigad and Leonardo de Moura and Soonho Kong},
title = {{T}heorem {P}roving in {L}ean},
year = {2017},
howpublished = {\url{https://leanprover.github.io/theorem_proving_in_lean/}}
}
@Book{ axler2015,
author = {Sheldon Axler},
title = {Linear algebra done right. 3rd ed.},
fjournal = {Undergraduate Texts in Mathematics},
journal = {Undergraduate Texts Math.},
issn = {0172-6056; 2197-5604/e},
edition = {3rd ed.},
isbn = {978-3-319-11079-0/hbk; 978-3-319-11080-6/ebook},
pages = {xvii + 340},
year = {2015},
publisher = {Springer}
}
@Manual{ banasiak,
author = {Banasiak},
title = {Banach Lattices in Applications},
organization = {University of Pretoria},
address = {Pretoria, South Africa}
}
@Book{ beals2004,
author = {Richard Beals},
title = {Analysis. An introduction},
publisher = {Cambridge University Press},
isbn = {0521600472},
year = {2004}
}
@Book{ behrends1979,
author = {Ehrhard {Behrends}},
title = {{M-structure and the Banach-Stone theorem}},
fjournal = {{Lecture Notes in Mathematics}},
journal = {{Lect. Notes Math.}},
issn = {0075-8434},
volume = {736},
year = {1979},
publisher = {Springer, Cham},
language = {English},
msc2010 = {46B20 46-02 46E40 46A40},
zbl = {0436.46013}
}
@Article{ bernstein1912,
author = {Bernstein, S.},
year = {1912},
title = {Démonstration du théorème de Weierstrass fondée sur le
calcul des probabilités},
journal = {Comm. Kharkov Math. Soc.},
volume = {13},
number = {1–2}
}
@InProceedings{ beylin1996,
author = "Beylin, Ilya and Dybjer, Peter",
editor = "Berardi, Stefano and Coppo, Mario",
title = "Extracting a proof of coherence for monoidal categories
from a proof of normalization for monoids",
booktitle = "Types for Proofs and Programs",
year = "1996",
publisher = "Springer Berlin Heidelberg",
address = "Berlin, Heidelberg",
pages = "47--61",
abstract = "This paper studies the problem of coherence in category
theory from a type-theoretic viewpoint. We first show how a
Curry-Howard interpretation of a formal proof of
normalization for monoids almost directly yields a
coherence proof for monoidal categories. Then we formalize
this coherence proof in intensional intuitionistic type
theory and show how it relies on explicit reasoning about
proof objects for intensional equality. This formalization
has been checked in the proof assistant ALF.",
isbn = "978-3-540-70722-6"
}
@Book{ billingsley1999,
author = {Billingsley, Patrick},
title = {Convergence of probability measures},
series = {Wiley Series in Probability and Statistics: Probability
and Statistics},
edition = {Second},
note = {A Wiley-Interscience Publication},
publisher = {John Wiley \& Sons, Inc., New York},
year = {1999},
pages = {x+277},
isbn = {0-471-19745-9},
mrclass = {60B10 (28A33 60F17)},
mrnumber = {1700749},
doi = {10.1002/9780470316962},
url = {https://doi.org/10.1002/9780470316962}
}
@Article{ birkhoff1942,
author = {Birkhoff, Garrett},
title = {Lattice, ordered groups},
journal = {Ann. of Math. (2)},
fjournal = {Annals of Mathematics. Second Series},
volume = {43},
year = {1942},
pages = {298--331},
issn = {0003-486X},
mrclass = {20.0X},
mrnumber = {6550},
mrreviewer = {H. Wallman},
doi = {10.2307/1968871},
url = {https://doi.org/10.2307/1968871}
}
@Book{ bollobas1986,
author = {Bollob\'{a}s, B\'{e}la},
title = {Combinatorics: Set Systems, Hypergraphs, Families of
Vectors, and Combinatorial Probability},
year = {1986},
isbn = {0521330599},
publisher = {Cambridge University Press}
}
@Book{ borceux-vol1,
title = {Handbook of Categorical Algebra: Volume 1, Basic Category
Theory},
author = {Borceux, Francis},
series = {Encyclopedia of Mathematics},
volume = {50},
year = {1994},
publisher = {Cambridge University Press}
}
@Book{ borceux-vol2,
title = {Handbook of Categorical Algebra: Volume 2, Categories and
Structures},
author = {Borceux, Francis},
series = {Encyclopedia of Mathematics},
volume = {51},
year = {1994},
publisher = {Cambridge University Press}
}
@Book{ borceux-vol3,
title = {Handbook of Categorical Algebra: Volume 3, Sheaf Theory},
author = {Borceux, Francis},
series = {Encyclopedia of Mathematics},
volume = {52},
year = {1994},
publisher = {Cambridge University Press}
}
@Book{ bosch-guntzer-remmert,
title = {Non-Archimedean Analysis : A Systematic Approach to Rigid
Analytic Geometry},
author = {S. Bosch and U. G{\"{u}}ntzer and R. Remmert},
series = {Grundlehren der mathematischen Wissenschaften},
volume = {261},
year = {1984},
publisher = {Springer-Verlag Berlin }
}
@Book{ bourbaki1966,
author = {Bourbaki, Nicolas},
title = {Elements of mathematics. {G}eneral topology. {P}art 1},
publisher = {Hermann, Paris; Addison-Wesley Publishing Co., Reading,
Mass.-London-Don Mills, Ont.},
year = {1966},
pages = {vii+437},
mrclass = {54.00 (00.00)},
mrnumber = {0205210}
}
@Book{ bourbaki1966b,
author = {Bourbaki, Nicolas},
title = {Elements of mathematics. {G}eneral topology. {P}art 2},
publisher = {Hermann, Paris; Addison-Wesley Publishing Co., Reading,
Mass.-London-Don Mills, Ont.},
year = {1966},
pages = {iv+363},
mrclass = {54-02 (00A05 54-01)},
mrnumber = {979295}
}
@Book{ bourbaki1968,
author = {Bourbaki, Nicolas},
title = {Lie groups and {L}ie algebras. {C}hapters 4--6},
series = {Elements of Mathematics (Berlin)},
note = {Translated from the 1968 French original by Andrew
Pressley},
publisher = {Springer-Verlag, Berlin},
year = {2002},
pages = {xii+300},
isbn = {3-540-42650-7},
mrclass = {17-01 (00A05 20E42 20F55 22-01)},
mrnumber = {1890629}
}
@Book{ bourbaki1975,
author = {Bourbaki, Nicolas},
title = {Lie groups and {L}ie algebras. {C}hapters 1--3},
series = {Elements of Mathematics (Berlin)},
note = {Translated from the French, Reprint of the 1989 English
translation},
publisher = {Springer-Verlag, Berlin},
year = {1998},
pages = {xviii+450},
isbn = {3-540-64242-0},
mrclass = {17Bxx (00A05 22Exx)},
mrnumber = {1728312}
}
@Book{ bourbaki1975b,
author = {Bourbaki, Nicolas},
title = {Lie groups and {L}ie algebras. {C}hapters 7--9},
series = {Elements of Mathematics (Berlin)},
note = {Translated from the 1975 and 1982 French originals by
Andrew Pressley},
publisher = {Springer-Verlag, Berlin},
year = {2005},
pages = {xii+434},
isbn = {3-540-43405-4},
mrclass = {17-01 (01A75 22-01)},
mrnumber = {2109105}
}
@Book{ bourbaki1981,
author = {Bourbaki, N.},
title = {Algebra. {II}. {C}hapters 4--7},
series = {Elements of Mathematics (Berlin)},
note = {Translated from the French by P. M. Cohn and J. Howie},
publisher = {Springer-Verlag, Berlin},
year = {1990},
pages = {vii+461},
isbn = {3-540-19375-8},
mrclass = {00A05 (12-01 13-01)},
mrnumber = {1080964}
}
@Book{ bourbaki1987,
author = {Bourbaki, N.},
title = {Topological vector spaces. {C}hapters 1--5},
series = {Elements of Mathematics (Berlin)},
note = {Translated from the French by H. G. Eggleston and S.
Madan},
publisher = {Springer-Verlag, Berlin},
year = {1987},
pages = {viii+364},
isbn = {3-540-13627-4},
mrclass = {46-02 (46-01 46Axx 47D15)},
mrnumber = {910295},
doi = {10.1007/978-3-642-61715-7},
url = {https://doi.org/10.1007/978-3-642-61715-7}
}
@Book{ bourbaki2007,
author = {Bourbaki, Nicolas},
edition = {Réimpression inchangée de l'édition originale de 1959},
series = {Eléments de mathématique},
title = {Algèbre. {C}hapitre IX},
isbn = {978-3-540-35338-6},
language = {fr},
number = {2},
publisher = {Springer},
year = {2007}
}
@Book{ boydVandenberghe2004,
author = {Stephen P. Boyd and Lieven Vandenberghe},
title = {Convex Optimization},
publisher = {Cambridge University Press},
year = {2004},
isbn = {978-0-521-83378-3},
url = {https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf}
}
@Book{ cabreragarciarodriguezpalacios2014,
author = {Miguel {Cabrera Garc\'{\i}a} and \'Angel {Rodr\'{\i}guez
Palacios}},
title = {{Non-associative normed algebras. Volume 1. The
Vidav-Palmer and Gelfand-Naimark theorems}},
fjournal = {{Encyclopedia of Mathematics and Its Applications}},
journal = {{Encycl. Math. Appl.}},
issn = {0953-4806},
volume = {154},
isbn = {978-1-107-04306-0; 978-1-107-33776-3},
pages = {xxii + 712},
year = {2014},
publisher = {Cambridge: Cambridge University Press},
language = {English},
doi = {10.1017/CBO9781107337763},
msc2010 = {46-02 17-02 46H70 46K70 46L70 17A15 17A80 17C65},
zbl = {1322.46003}
}
@Article{ cadiou1972,
title = {Recursive definitions of partial functions and their
computations},
doi = {10.1145/942580.807072},
number = {14},
journal = {ACM SIGACT News},
author = {Cadiou, Jean Marie Cadiou and Manna, Zohar},
year = {1972},
month = {Jan},
pages = {58–65}
}
@Book{ calugareanu,
author = {C\v{a}lug\v{a}reanu, Grigore},
year = {2000},
month = {01},
pages = {},
title = {Lattice Concepts of Module Theory},
doi = {10.1007/978-94-015-9588-9}
}
@Article{ CARBONI1993145,
author = {Aurelio Carboni and Stephen Lack and R.F.C. Walters},
doi = {https://doi.org/10.1016/0022-4049(93)90035-R},
issn = {0022-4049},
journal = {Journal of Pure and Applied Algebra},
number = {2},
pages = {145-158},
title = {Introduction to extensive and distributive categories},
url = {https://www.sciencedirect.com/science/article/pii/002240499390035R},
volume = {84},
year = {1993},
bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/002240499390035R},
bdsk-url-2 = {https://doi.org/10.1016/0022-4049(93)90035-R}
}
@Article{ carneiro2015arithmetic,
title = {Arithmetic in Metamath, Case Study: Bertrand's Postulate},
author = {Carneiro, Mario},
journal = {arXiv preprint arXiv:1503.02349},
year = {2015}
}
@Misc{ carneiro2018matiyasevic,
title = {A {L}ean formalization of {M}atiyasevi{\v c}'s theorem},
author = {Mario Carneiro},
year = {2018},
eprint = {1802.01795},
archiveprefix = {arXiv},
primaryclass = {math.LO}
}
@InProceedings{ carneiro2019,
author = {Mario M. Carneiro},
editor = {John Harrison and John O'Leary and Andrew Tolmach},
title = {Formalizing Computability Theory via Partial Recursive
Functions},
booktitle = {10th International Conference on Interactive Theorem
Proving, {ITP} 2019, September 9-12, 2019, Portland, OR,
{USA}},
series = {LIPIcs},
volume = {141},
pages = {12:1--12:17},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum f{\"{u}}r Informatik},
year = {2019},
url = {https://doi.org/10.4230/LIPIcs.ITP.2019.12},
doi = {10.4230/LIPIcs.ITP.2019.12},
timestamp = {Fri, 27 Sep 2019 15:57:06 +0200},
biburl = {https://dblp.org/rec/conf/itp/Carneiro19.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@Article{ cassels1950,
author = {Cassels, J. W. S.},
title = {Some metrical theorems in {D}iophantine approximation.
{I}},
journal = {Proc. Cambridge Philos. Soc.},
fjournal = {Proceedings of the Cambridge Philosophical Society},
volume = {46},
year = {1950},
pages = {209--218},
issn = {0008-1981},
mrclass = {10.0X},
mrnumber = {36787},
mrreviewer = {P. Erd\H{o}s},
doi = {10.1017/s0305004100025676},
url = {https://doi.org/10.1017/s0305004100025676}
}
@Book{ cassels1967algebraic,
title = {Algebraic number theory},
author = {Cassels, John William Scott and Fr{\"o}hlich, Albrecht},
booktitle = {Proceedings of an instructional conference organized by
the {L}ondon {M}athematical {S}ociety (a {NATO} {A}dvanced
{S}tudy {I}nstitute) with the support of the
{I}nternational {M}athematical {U}nion},
editor = {Cassels, John William Scott and Fr\"{o}hlich, Albrecht},
publisher = {Academic Press, London; Thompson Book Co., Inc.,
Washington, D.C.},
year = {1967},
pages = {xviii+366},
mrclass = {00.04 (10.00)}
}
@InProceedings{ Chou1994,
author = {Chou, Ching-Tsun},
booktitle = {Higher Order Logic Theorem Proving and Its Applications},
title = {A formal theory of undirected graphs in higher-order
logic},
year = {1994},
address = {Berlin, Heidelberg},
editor = {Melham, Thomas F. and Camilleri, Juanito},
pages = {144--157},
publisher = {Springer Berlin Heidelberg},
isbn = {978-3-540-48803-3}
}
@Book{ chu2012,
author = {Cho-Ho {Chu}},
title = {{Jordan structures in geometry and analysis}},
fjournal = {{Cambridge Tracts in Mathematics}},
journal = {{Camb. Tracts Math.}},
issn = {0950-6284},
volume = {190},
isbn = {978-1-107-01617-0},
pages = {x + 261},
year = {2012},
publisher = {Cambridge: Cambridge University Press},
language = {English},
msc2010 = {17-02 17C65 17C37 46H70 53C35 46K70 32M15},
zbl = {1238.17001}
}
@InProceedings{ CL21,
author = {Commelin, Johan and Lewis, Robert Y.},
title = {Formalizing the Ring of Witt Vectors},
year = {2021},
isbn = {9781450382991},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/3437992.3439919},
doi = {10.1145/3437992.3439919},
abstract = {The ring of Witt vectors W R over a base ring R is an
important tool in algebraic number theory and lies at the
foundations of modern p-adic Hodge theory. W R has the
interesting property that it constructs a ring of
characteristic 0 out of a ring of characteristic p > 1,
and it can be used more specifically to construct from a
finite field containing ℤ/pℤ the corresponding
unramified field extension of the p-adic numbers ℚp
(which is unique up to isomorphism). We formalize the
notion of a Witt vector in the Lean proof assistant, along
with the corresponding ring operations and other algebraic
structure. We prove in Lean that, for prime p, the ring of
Witt vectors over ℤ/pℤ is isomorphic to the ring of
p-adic integers ℤp. In the process we develop idioms to
cleanly handle calculations of identities between
operations on the ring of Witt vectors. These calculations
are intractable with a naive approach, and require a proof
technique that is usually skimmed over in the informal
literature. Our proofs resemble the informal arguments
while being fully rigorous.},
booktitle = {Proceedings of the 10th ACM SIGPLAN International
Conference on Certified Programs and Proofs},
pages = {264–277},
numpages = {14},
keywords = {ring theory, formal math, proof assistant, Lean, number
theory},
location = {Virtual, Denmark},
series = {CPP 2021}
}
@Book{ clark_gon,
author = {Pete L. Clark},
title = {Geometry of Numbers with Applications to Number Theory},
url = {http://alpha.math.uga.edu/~pete/geometryofnumbers.pdf}
}
@Book{ conway2001,
author = {Conway, J. H.},
title = {On numbers and games},
edition = {Second},
publisher = {A K Peters, Ltd., Natick, MA},
year = {2001},
pages = {xii+242},
isbn = {1-56881-127-6},
mrclass = {00A08 (05-01 91A05)},
mrnumber = {1803095}
}
@Book{ coxlittleoshea1997,
author = {David A. Cox and John Little and Donal O'Shea},
title = {Ideals, varieties, and algorithms - an introduction to
computational algebraic geometry and commutative algebra
{(2.} ed.)},
series = {Undergraduate texts in mathematics},
publisher = {Springer},
year = {1997},
isbn = {978-0-387-94680-1}
}
@Article{ crans2017,
author = {Crans, Alissa S. and Mukherjee, Sujoy and Przytycki,
J\'{o}zef H.},
title = {On homology of associative shelves},
journal = {J. Homotopy Relat. Struct.},
fjournal = {Journal of Homotopy and Related Structures},
volume = {12},
year = {2017},
number = {3},
pages = {741--763},
issn = {2193-8407},
mrclass = {18G60 (20M32 20N02 57M25)},
mrnumber = {3691304},
mrreviewer = {Mahender Singh},
doi = {10.1007/s40062-016-0164-9},
url = {https://doi.org/10.1007/s40062-016-0164-9}
}
@Book{ davey_priestley,
author = {Davey, B. A. and Priestley, H. A.},
title = {Introduction to lattices and order},
edition = {Second},
publisher = {Cambridge University Press, New York},
year = {2002},
pages = {xii+298},
isbn = {0-521-78451-4},
mrclass = {06-01 (68Q55)},
mrnumber = {1902334},
mrreviewer = {T. S. Blyth},
doi = {10.1017/CBO9780511809088},
url = {https://doi.org/10.1017/CBO9780511809088}
}
@InProceedings{ deligne_formulaire,
author = {Deligne, P.},
title = {Courbes elliptiques: formulaire d'apr\`es {J}. {T}ate},
booktitle = {Modular functions of one variable, {IV} ({P}roc.
{I}nternat. {S}ummer {S}chool, {U}niv. {A}ntwerp,
{A}ntwerp, 1972)},
pages = {53--73. Lecture Notes in Math., Vol. 476},
year = {1975},
mrclass = {14K15 (10D05)},
mrnumber = {0387292},
mrreviewer = {Jacques Velu}
}
@InProceedings{ demoura2015lean,
author = {de Moura, Leonardo and Kong, Soonho and Avigad, Jeremy and
van Doorn, Floris and von Raumer, Jakob},
editor = {Felty, Amy P. and Middeldorp, Aart},
title = {The Lean Theorem Prover (System Description)},
booktitle = {Automated Deduction - CADE-25},
year = {2015},
publisher = {Springer International Publishing},
address = {Cham},
pages = {378--388},
isbn = {978-3-319-21401-6}
}
@Article{ dold1958,
author = {Dold, Albrecht},
title = {Homology of symmetric products and other functors of
complexes},
journal = {Ann. of Math. (2)},
fjournal = {Annals of Mathematics. Second Series},
volume = {68},
year = {1958},
pages = {54--80},
issn = {0003-486X},
mrclass = {55.00},
mrnumber = {97057},
mrreviewer = {Sze-tsen Hu},
doi = {10.2307/1970043}
}
@Misc{ dupuis-lewis-macbeth2022,
title = {Formalized functional analysis with semilinear maps},
author = {Frédéric Dupuis and Robert Y. Lewis and Heather
Macbeth},
year = {2022},
eprint = {2202.05360},
archiveprefix = {arXiv},
primaryclass = {cs.LO}
}
@Article{ dyckhoff_1992,
author = {Dyckhoff, Roy},
title = {Contraction-free sequent calculi for intuitionistic
logic},
journal = {Journal of Symbolic Logic},
number = {3},
year = {1992},
pages = {795–807},
volume = {57},
publisher = {Cambridge University Press},
doi = {10.2307/2275431}
}
@Book{ EinsiedlerWard2017,
author = {Einsiedler, Manfred and Ward, Thomas},
title = {Functional Analysis, Spectral Theory, and Applications},
year = 2017,
publisher = {Springer},
doi = {10.1007/978-3-319-58540-6}
}
@Book{ Eisenbud1995,
title = "Commutative algebra",
author = "Eisenbud, David",
publisher = "Springer",
series = "Graduate Texts in Mathematics",
month = mar,
year = 1995,
address = "New York, NY",
language = "en",
isbn = {978-0-387-94268-1},
doi = {10.1007/978-1-4612-5350-1}
}
@Book{ Elephant,
title = {Sketches of an Elephant – A Topos Theory Compendium},
author = {Peter Johnstone},
year = {2002},
publisher = {Oxford University Press}
}
@Book{ engel1997,
title = {Sperner theory},
author = {Engel, Konrad},
publisher = {Cambridge University Press},
place = {Cambridge},
year = {1997}
}
@Article{ erdosrenyisos,
author = {P. Erd\"os, A.R\'enyi, and V. S\'os},
title = {On a problem of graph theory},
journal = {Studia Sci. Math.},
number = {1},
year = {1966},
pages = {215--235},
url = {https://www.renyi.hu/~p_erdos/1966-06.pdf}
}
@Article{ etemadi_strong_law,
author = {Etemadi, Nasrollah},
title = {An elementary proof of the strong law of large numbers},
journal = {Z. Wahrsch. Verw. Gebiete},
fjournal = {Zeitschrift f\"{u}r Wahrscheinlichkeitstheorie und
Verwandte Gebiete},
volume = {55},
year = {1981},
number = {1},
pages = {119--122},
issn = {0044-3719},
mrclass = {60F15 (60B12)},
mrnumber = {606010},
mrreviewer = {Robert L. Taylor},
doi = {10.1007/BF01013465},
url = {https://doi.org/10.1007/BF01013465}
}
@Book{ Federer1996,
author = {Herbert Federer},
title = {Geometric Measure Theory},
series = {Classics in Mathematics},
year = {1996},
publisher = {Springer-Verlag Berlin Heidelberg},
issn = {1431-0821},
doi = {10.1007/978-3-642-62010-2},
numpages = {677}
}
@Article{ FennRourke1992,
author = {Fenn, Roger and Rourke, Colin},
journal = {Journal of Knot Theory and its Ramifications},
title = {Racks and links in codimension two},
year = {1992},
issn = {0218-2165},
number = {4},
pages = {343--406},
volume = {1},
doi = {10.1142/S0218216592000203},
keywords = {57M25 (57N10)},
mrnumber = {1194995}
}
@InProceedings{ flypitch_cpp,
doi = {10.1145/3372885.3373826},
url = {https://doi.org/10.1145/3372885.3373826},
year = {2020},
month = jan,
publisher = {{ACM}},
author = {Jesse Michael Han and Floris van Doorn},
title = {A formal proof of the independence of the continuum
hypothesis},
booktitle = {Proceedings of the 9th {ACM} {SIGPLAN} International
Conference on Certified Programs and Proofs}
}
@InProceedings{ flypitch_itp,
author = {Jesse Michael Han and Floris van Doorn},
title = {{A Formalization of Forcing and the Unprovability of the
Continuum Hypothesis}},
booktitle = {10th International Conference on Interactive Theorem
Proving (ITP 2019)},
pages = {19:1--19:19},
series = {Leibniz International Proceedings in Informatics
(LIPIcs)},
isbn = {978-3-95977-122-1},
issn = {1868-8969},
year = {2019},
volume = {141},
editor = {John Harrison and John O'Leary and Andrew Tolmach},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
url = {http://drops.dagstuhl.de/opus/volltexte/2019/11074},
urn = {urn:nbn:de:0030-drops-110742},
doi = {10.4230/LIPIcs.ITP.2019.19},
annote = {Keywords: Interactive theorem proving, formal
verification, set theory, forcing, independence proofs,
continuum hypothesis, Boolean-valued models, Lean}
}
@Book{ fremlin_vol2,
author = {Fremlin, David H.},
title = {Measure theory. {V}ol. 2},
note = {Broad foundations, 2010 edition},
publisher = {Torres Fremlin, Colchester},
year = {2010},
isbn = {0-9538129-2-8}
}
@Book{ fremlin_vol4,
author = {Fremlin, David H.},
title = {Measure theory. {V}ol. 4},
note = {Topological Measure Spaces},
publisher = {Torres Fremlin, Colchester},
year = {2003}
}
@Book{ freyd1964abelian,
title = {Abelian categories},
author = {Freyd, Peter J},
series = {Harper's Series in Modern Mathematics},
year = {1964},
publisher = {Harper \& Row New York}
}
@Book{ friedmanscarr2005,
author = {Yaakov {Friedman}},
title = {{Physical applications of homogeneous balls. With the
assistance of Tzvi Scarr}},
fjournal = {{Progress in Mathematical Physics}},
journal = {{Prog. Math. Phys.}},
issn = {1544-9998},
volume = {40},
isbn = {0-8176-3339-1},
pages = {xxiv + 279},
year = {2005},
publisher = {Boston, MA: Birkh\"auser},
language = {English},
msc2010 = {46-02 17C65 46L60 46G20 46L70 83A05},
zbl = {1080.46001}
}
@Book{ fuchs1963,
author = {Fuchs, L.},
title = {Partially ordered algebraic systems},
publisher = {Pergamon Press, Oxford-London-New York-Paris;
Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo
Alto, Calif.-London},
year = {1963},
pages = {ix+229},
mrclass = {06.00 (20.00)},
mrnumber = {0171864},
mrreviewer = {P. F. Conrad}
}
@InProceedings{ fuerer-lochbihler-schneider-traytel2020,
author = {Basil F{\"{u}}rer and Andreas Lochbihler and Joshua
Schneider and Dmitriy Traytel},
editor = {Nicolas Peltier and Viorica Sofronie{-}Stokkermans},
title = {Quotients of Bounded Natural Functors},
booktitle = {Automated Reasoning - 10th International Joint Conference,
{IJCAR} 2020, Paris, France, July 1-4, 2020, Proceedings,
Part {II}},
series = {Lecture Notes in Computer Science},
volume = {12167},
pages = {58--78},
publisher = {Springer},
year = {2020},
url = {https://doi.org/10.1007/978-3-030-51054-1\_4},
doi = {10.1007/978-3-030-51054-1\_4},
timestamp = {Mon, 06 Jul 2020 09:05:32 +0200},
biburl = {https://dblp.org/rec/conf/cade/FurerLST20.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@Article{ furedi-loeb1994,
author = {Zolt\'an {F\"uredi} and Peter A. {Loeb}},
journal = {{Proc. Am. Math. Soc.}},
title = {{On the best constant for the Besicovitch covering
theorem}},
year = {1994},
issn = {0002-9939},
number = {4},
pages = {1063--1073},
volume = {121},
doi = {10.2307/2161215},
fjournal = {{Proceedings of the American Mathematical Society}},
language = {English},
msc2010 = {28A75 05B40 51M16},
publisher = {American Mathematical Society (AMS), Providence, RI},
zbl = {0802.28002}
}
@Book{ gabriel-zisman-1967,
author = {Gabriel, P. and Zisman, M.},
title = {Calculus of fractions and homotopy theory},
series = {Ergebnisse der Mathematik und ihrer Grenzgebiete, Band
35},
publisher = {Springer-Verlag New York, Inc., New York},
year = {1967},
pages = {x+168}
}
@Article{ Gallagher1961,
author = {Gallagher, Patrick},
title = {Approximation by reduced fractions},
journal = {J. Math. Soc. Japan},
fjournal = {Journal of the Mathematical Society of Japan},
volume = {13},
year = {1961},
pages = {342--345},
issn = {0025-5645},
mrclass = {10.30},
mrnumber = {133297},
mrreviewer = {J. W. S. Cassels},
doi = {10.2969/jmsj/01340342},
url = {https://doi.org/10.2969/jmsj/01340342}
}
@InProceedings{ Gallier2011Notes,
title = {Notes on Differential Geometry and Lie Groups},
author = {J. Gallier and J. Quaintance},
year = {2011},
url = {https://www.cis.upenn.edu/~cis610/diffgeom-n.pdf}
}
@Article{ ghys87:groupes,
author = {Étienne Ghys},
title = {Groupes d'homéomorphismes du cercle et cohomologie
bornée},
journal = {Contemporary Mathematics},
year = 1987,
volume = 58,
number = {III},
pages = {81-106},
doi = {10.1090/conm/058.3/893858},
language = {french}
}
@Article{ gibbons2009,
title = {The essence of the Iterator pattern},
volume = {19},
issn = {0956-7968, 1469-7653},
url = {https://www.cambridge.org/core/product/identifier/S0956796809007291/type/journal_article},
doi = {10.1017/S0956796809007291},
language = {en},
number = {3-4},
urldate = {2021-10-24},
journal = {Journal of Functional Programming},
author = {Gibbons, Jeremy and Oliveira, BRUNO C. d. S.},
month = jul,
year = {2009},
pages = {377--402}
}
@Book{ GierzEtAl1980,
author = {Gierz, Gerhard and Hofmann, Karl Heinrich and Keimel,
Klaus and Lawson, Jimmie D. and Mislove, Michael W. and
Scott, Dana S.},
title = {A compendium of continuous lattices},
publisher = {Springer-Verlag, Berlin-New York},
year = {1980},
pages = {xx+371},
isbn = {3-540-10111-X},
mrclass = {06B30 (03G10 30G30 54H12)},
mrnumber = {614752},
mrreviewer = {James W. Lea, Jr.}
}