paper-filmat.bib

@incollection{bauer:int-mathematics,
  author = {Bauer, A.},
  title = {Intuitionistic mathematics and realizability in the physical world},
  booktitle = {A Computable Universe},
  publisher = {World Scientific Pub Co},
  editor = {Zenil, H.},
  year = {2012}}

@misc{bauer:video,
  author = {Bauer, A.},
  title = {Five stages of accepting constructive mathematics},
  year = {2013},
  note = {Lecture at the Institute for Advanced Study, \url{https://video.ias.edu/members/1213/0318-AndrejBauer}}}

@unpublished{melikhov:intuitionistic-logic,
  author = {Melikhov, S.},
  title = {Mathematical semantics of intuitionistic logic},
  year = {2015},
  note = {\url{https://arxiv.org/abs/1504.03380}}}

@book{mines-richman-ruitenburg:constructive-algebra,
  title = {A Course in Constructive Algebra},
  author = {Mines, R. and Richman, F. and Ruitenburg, W.},
  series = {Universitext},
  year = {1988},
  publisher = {Springer}}

@book{lombardi-quitte:constructive-algebra,
  author = {Lombardi, H. and Quitté, C.},
  title = {Commutative Algebra: Constructive Methods},
  year = {2015},
  publisher = {Springer}}

@book{bishop-bridges:constructive-analysis,
  author = {Bishop, E. and Bridges, D.},
  title = {Constructive Analysis},
  publisher = {Springer},
  year = {1985}}

@article{bauer:injection,
  author = {Bauer, A.},
  title = {{An injection from the Baire space to natural numbers}},
  journal = {Math. Structures Comput. Sci.},
  volume = {25},
  number = {7},
  pages = {1484--1489},
  year = {2015}}

@article{hamkins-lewis:ittm,
  title = {{Infinite time Turing machines}},
  author = {Hamkins, J. and Lewis, A.},
  journal = {J. Symbolic Logic},
  volume = {65},
  number = {2},
  year = {2000},
  pages = {567--604}}

@phdthesis{blechschmidt:phd,
  author = {Blechschmidt, I.},
  title = {Using the internal language of toposes in algebraic geometry},
  year = {2017},
  school = {University of Augsburg},
  note = {\url{https://arxiv.org/abs/2111.03685}}}

@unpublished{blechschmidt:nullstellensatz,
  author = {Blechschmidt, I.},
  title = {{A general Nullstellensatz for generalized spaces}},
  year = {2020},
  note = {\url{https://rawgit.com/iblech/internal-methods/master/paper-qcoh.pdf}}}

@article{pospisil:ultrafilters,
  author = {Pospíšil, B.},
  title = {Remark on bicompact spaces},
  journal = {Ann. of Math.},
  volume = {38},
  number = {4},
  year = {1937},
  pages = {845--846}}

@misc{tao:cheap-nsa,
  author = {Tao, T.},
  title = {A cheap version of nonstandard analysis},
  year = {2012},
  note = {Blog post, \url{https://terrytao.wordpress.com/2012/04/02/a-cheap-version-of-nonstandard-analysis/}}}

@book{kock:sdg,
  author = {Kock, A.},
  title = {Synthetic Differential Geometry},
  year = {2006},
  publisher = {Cambridge University Press},
  edition = {2},
  series = {London Math Soc. Lecture Note Ser.},
  number = {333},
  note = {\url{http://home.math.au.dk/kock/sdg99.pdf}}}

@book{moerdijk-reyes:models,
  author = {Moerdijk, I. and Reyes, G.},
  title = {Models for Smooth Infinitesimal Analysis},
  year = {1991},
  publisher = {Springer}}

@incollection{kock:new-methods,
  author = {Kock, A.},
  title = {New methods for old spaces: synthetic differential geometry},
  booktitle = {New Spaces in Mathematics and Physics},
  volume = {1},
  editor = {Anel, M. and Cartren, G.},
  year = {2020},
  publisher = {Cambridge University Press},
  note = {\url{https://arxiv.org/abs/1610.00286}}}

@article{lambek:incompatible,
  author = {Lambek, J.},
  title = {Are the traditional philosophies of mathematics really incompatible?},
  journal = {Math. Intelligencer},
  year = {1994},
  volume = {16},
  number = {1},
  pages = {56--62}}

@article{couture-lambek:reflections,
  author = {Couture, J. and Lambek, J.},
  title = {Philosophical reflections on the foundations of mathematics},
  journal = {Erkenntnis},
  year = {1991},
  volume = {34},
  pages = {187--209}}

@article{butterfield-hamilton-isham:bohr,
  author = {Butterfield, J. and Hamilton, J. and Isham, C.},
  title = {{A topos perspective on the Kochen--Specker theorem, I. quantum states as generalized valuations}},
  journal = {Internat. J. Theoret. Phys.},
  volume = {37},
  number = {11},
  pages = {2669--2733},
  year = {1998}}

@article{heunen-landsman-spitters:aqt,
  author = {Heunen, C. and Landsman, N. and Spitters, B.},
  title = {A topos for algebraic quantum theory},
  year = {2009},
  journal = {Comm. Math. Phys.},
  volume = {291},
  number = {1},
  pages = {63--110}}

@misc{vickers:sketches,
  author = {Vickers, S.},
  title = {Sketches for arithmetic universes},
  year = {2016},
  note = {\url{https://arxiv.org/abs/1608.01559}}}

@article{maietti:au,
  author = {Maietti, M.},
  title = {Joyal's arithmetic universes as list-arithmetic pretoposes},
  year = {2010},
  journal = {Theory Appl. Categ.},
  volume = {23},
  number = {3},
  pages = {39--83}}

@article{maietti-vickers:induction,
  author = {Maietti, M. and Vickers, S.},
  title = {An induction principle for consequence in arithmetic universes},
  journal = {J. Pure Appl. Algebra},
  volume = {216},
  number = {8--9},
  year = {2012},
  pages = {2049--2067}}

@book{caramello:tst,
  author = {Caramello, O.},
  title = {Theories, Sites, Toposes: Relating and studying mathematical theories through topos-theoretic `bridges'},
  publisher = {Oxford University Press},
  year = {2018}}

@inproceedings{kreisel-lacombe-shoenfield:cont,
  author = {Kreisel, G. and Lacombe, D. and Shoenfield, J.},
  title = {Partial recursive functionals and effective operations},
  booktitle = {Constructivity in mathematics: proceedings of the colloquium held in Amsterdam, 1957},
  year = {1959},
  editor = {Heyting, A.},
  pages = {290--297},
  publisher = {North-Holland}}

@article{ceitin:cont,
  author = {Ceĭtin, G.},
  title = {Algorithmic operators in constructive metric spaces},
  journal = {Tr. Mat. Inst. Steklova},
  volume = {67},
  pages = {295--361},
  year = {1962}}

@book{longley-normann:higher-order-computability,
  author = {Longley, J. and Normann, D.},
  title = {Higher-Order Computability},
  publisher = {Springer},
  series = {Theory and Applications of Computability},
  year = {2015}}

@unpublished{berg-oosten:arithmetic,
  author = {van den Berg, B. and van Oosten, J.},
  title = {Arithmetic is categorical},
  year = {2011},
  note = {\url{https://www.staff.science.uu.nl/~ooste110/realizability/arithcat.pdf}}}

@article{tennenbaum:models,
  author = {Tennenbaum, S.},
  title = {Non-Archimedean models for arithmetic},
  year = {1959},
  journal = {Notices Amer. Math. Soc.},
  volume = {6},
  pages = {270}}

@book{oosten:realizability,
  author = {van Oosten, J.},
  title = {Realizability: An Introduction to its Categorical Side},
  year = {2008},
  series = {Stud. Logic Found. Math.},
  volume = {152},
  publisher = {Elsevier}}

@article{awodey-butz-simpson-streicher:bist,
  author = {Awodey, S. and Butz, C. and Simpson, A. and Streicher, T.},
  title = {Relating first-order set theories, toposes and categories of classes},
  year = {2014},
  pages = {428--502},
  volume = {165},
  journal = {Ann. Pure Appl. Logic}}

@article{fourman:sheaf-models,
  author = {Fourman, M.},
  title = {Sheaf models for set theory},
  journal = {J. Pure Appl. Algebra},
  volume = {19},
  year = {1980},
  pages = {91--101}}

@article{streicher:forcizf,
  author = {Streicher, T.},
  title = {Forcing for {\textsc{izf}} in sheaf toposes},
  journal = {Georgian Math. J.},
  volume = {16},
  issue = {1},
  year = {2009},
  pages = {203--209}}

@article{escardo:omniscience,
  author = {Escardó, M.},
  title = {Infinite sets that satisfy the principle of omniscience in any variety of constructive mathematics},
  journal = {J. Symbolic Logic},
  volume = {78},
  number = {3},
  year = {2013},
  pages = {764--784}}

@article{mclarty:structuralism,
  author = {McLarty, C.},
  title = {Exploring categorical structuralism},
  year = {2004},
  journal = {Philos. Math.},
  volume = {12},
  number = {1},
  pages = {37--53}}

@incollection{barton-friedman:structures,
  author = {Barton, N. and Friedman, S.-D.},
  title = {Set theory and structures},
  booktitle = {Reflections on the Foundations of Mathematics},
  editor = {Centrone, S. and Kant, D. and Sarikaya, D.},
  series = {Synth. Libr.},
  volume = {407},
  year = {2019},
  publisher = {Springer},
  pages = {223--253}}

@article{marquis:foundations,
  author = {Marquis, J.-P.},
  title = {Categorical foundations of mathematics},
  journal = {Rev. Symb. Log.},
  volume = {6},
  number = {1},
  year = {2013},
  pages = {51--75}}

@inproceedings{hyland:effective-topos,
  author = {Hyland, M.},
  title = {The ef{}fective topos},
  editor = {Troelstra, A. S. and van Dalen, D.},
  booktitle = {The L. E. J. Brouwer Centenary Symposium},
  publisher = {North-Holland},
  year = {1982},
  pages = {165--216}}

@techreport{phoa:effective,
  author = {Phoa, W.},
  title = {An introduction to fibrations, topos theory, the ef{}fective topos and modest sets},
  institution = {University of Edinburgh},
  year = {1992},
  note = {\url{http://www.lfcs.inf.ed.ac.uk/reports/92/ECS-LFCS-92-208/}}}

@misc{bauer:c2c,
  author = {Bauer, A.},
  title = {Realizability as the connection between computable and constructive mathematics},
  year = {2005},
  note = {\url{http://math.andrej.com/asset/data/c2c.pdf}}}

@article{leinster:introduction,
  author = {Leinster, T.},
  title = {An informal introduction to topos theory},
  journal = {Publications of the nLab},
  volume = {1},
  number = {1},
  year = {2011}}

@book{moerdijk-maclane:sheaves-logic,
  author = {Mac Lane, S. and Moerdijk, I.},
  title = {Sheaves in Geometry and Logic: a First Introduction to Topos Theory},
  publisher = {Springer},
  series = {Universitext},
  year = {1992}}

@book{goldblatt:topoi,
  author = {Goldblatt, R.},
  title = {Topoi: The Categorical Analysis of Logic},
  year = {1984},
  publisher = {Elsevier},
  series = {Stud. Logic Found. Math.},
  volume = {98}}

@unpublished{caramello:preliminaries,
  author = {Caramello, O.},
  title = {Topos-theoretic background},
  year = {2014},
  note = {\url{https://www.oliviacaramello.com/Unification/ToposTheoreticPreliminariesOliviaCaramello.pdf}}}

@misc{streicher:ctcl,
  author = {Streicher, T.},
  title = {Introduction to category theory and categorical logic},
  year = {2004},
  note = {\url{https://www.mathematik.tu-darmstadt.de/~streicher/CTCL.pdf}}}

@misc{shulman:categorical-logic,
  author = {Shulman, M.},
  title = {{Categorical logic from a categorical point of view (draft for AARMS Summer School 2016)}},
  year = {2016},
  note = {\url{https://mikeshulman.github.io/catlog/catlog.pdf}}}

@book{borceux:handbook3,
  author = {Borceux, F.},
  title = {Handbook of Categorical Algebra: Volume 3, Sheaf Theory},
  series = {Encyclopedia Math. Appl.},
  year = {1994},
  publisher = {Cambridge University Press}}

@book{johnstone:elephant,
  author = {Johnstone, P. T.},
  title = {Sketches of an Elephant: A Topos Theory Compendium},
  year = {2002},
  publisher = {Oxford University Press}}

@incollection{sep:category-theory,
 author    = {Marquis, J.-P.},
 title     = {Category theory},
 booktitle = {The Stanford Encyclopedia of Philosophy},
 editor    = {Zalta, E.},
 note      = {\url{https://plato.stanford.edu/archives/fall2019/entries/category-theory/}},
 year      = {2019},
 edition   = {Fall 2019},
 publisher = {Metaphysics Research Lab, Stanford University}}

@incollection{crosilla:predicativity,
  author = {Crosilla, L.},
  title = {Exploring predicativity},
  booktitle = {Proof and Computation},
  editor = {Mainzer, K. and Schuster, P. and Schwichtenberg, H.},
  publisher = {World Scientific},
  year = {2018},
  pages = {83--108}}

@article{hamkins:multiverse,
  author = {Hamkins, J.},
  title = {The set-theoretic multiverse},
  journal = {Rev. Symb. Log.},
  volume = {5},
  issue = {3},
  year = {2012},
  pages = {416-449}}

@unpublished{fabert:non-squeezing,
  author = {Fabert, O.},
  title = {Infinite-dimensional symplectic non-squeezing using non-standard analysis},
  year = {2015},
  note = {\url{https://arxiv.org/abs/1501.05905}}}

@unpublished{fabert:floer,
  author = {Fabert, O.},
  title = {{Floer theory for Hamiltonian PDE using model theory}},
  year = {2015},
  note = {\url{https://arxiv.org/abs/1507.00482}}}

@phdthesis{menni:exact,
  author = {Menni, M.},
  title = {Exact completions and toposes},
  year = {2000},
  school = {University of Edinburgh},
  note = {\url{https://www.lfcs.inf.ed.ac.uk/reports/00/ECS-LFCS-00-424/ECS-LFCS-00-424.pdf}}}

@misc{blechschmidt:generic-freeness,
  author = {Blechschmidt, I.},
  title = {{An elementary and constructive proof of Grothendieck's generic freeness lemma}},
  year = {2018},
  note = {\url{https://arxiv.org/abs/1807.01231}}}

@book{artin-grothendieck-verdier:topos,
  author = {Artin, M. and Grothendieck, A. and Verdier, J.},
  title = {Théorie des topos et cohomologie étale des schémas (SGA 4)},
  publisher = {Springer},
  year = {1972},
  series = {Lecture Notes in Math.},
  volume = {269, 270, 305}}

@misc{milne:etale,
  author = {Milne, J.},
  title = {Lectures on Étale Cohomology},
  year = {2013},
  note = {\url{https://www.jmilne.org/math/CourseNotes/LEC.pdf}}}

@book{hakim:relative-schemes,
  author = {Hakim, M.},
  title = {Topos annelés et schémas relatifs},
  series = {Ergeb. Math. Grenzgeb.},
  volume = {64},
  year = {1972},
  publisher = {Springer}}

@unpublished{shulman:stack,
  author = {Shulman, M.},
  title = {Stack semantics and the comparison of material and structural set theories},
  year = {2010},
  note = {\url{https://arxiv.org/abs/1004.3802}}}

@article{mclarty:history,
  author = {McLarty, C.},
  title = {The uses and abuses of the history of topos theory},
  journal = {British J. Philos. Sci.},
  volume = {41},
  number = {3},
  year = {1990},
  pages = {351--375}}