Practical Foundations of Mathematics
http://www.paultaylor.eu/prafm/
http://www.paultaylor.eu/prafm/
Relating first-order set theories, toposes and categories of classes
http://www.phil.cmu.edu/projects/ast/Papers/Awodey-Butz-Simpson-Streicher-APAL-2013.pdf
http://www.phil.cmu.edu/projects/ast/Papers/Awodey-Butz-Simpson-Streicher-APAL-2013.pdf
Infinite Time Turing Machines
https://arxiv.org/pdf/math/9808093.pdf
https://arxiv.org/pdf/math/9808093.pdf
An introduction to locally finitely presentable categories
https://pi.math.cornell.edu/~maru/documents/locally_finitely_presentable_cats.pdf
https://pi.math.cornell.edu/~maru/documents/locally_finitely_presentable_cats.pdf
1460059215690.pdf
3.7 MB
Conceptual Mathematics
A new pass at the NF consistency proof
https://randall-holmes.github.io/Nfproof/newattempt.pdf
https://randall-holmes.github.io/Nfproof/newattempt.pdf
A suite of cool logic programs
https://xorshammer.com/2009/05/14/a-suite-of-cool-logic-programs/
https://xorshammer.com/2009/05/14/a-suite-of-cool-logic-programs/
XOR's Hammer
A Suite of Cool Logic Programs
You may have heard about the Tarski-Seidenberg theorem, which says that the first-order theory of the reals is decidable, that the first-order theory of the complex numbers is similarly decidable, …
The relative efficiency of propositional proof systems
https://www.cs.toronto.edu/~sacook/homepage/cook_reckhow.pdf
https://www.cs.toronto.edu/~sacook/homepage/cook_reckhow.pdf
Restricted Set-theoretic Definitions in Arithmetic
https://www.ams.org/journals/proc/1958-009-02/S0002-9939-1958-0093479-4/S0002-9939-1958-0093479-4.pdf
https://www.ams.org/journals/proc/1958-009-02/S0002-9939-1958-0093479-4/S0002-9939-1958-0093479-4.pdf
Real Analysis in Reverse
http://faculty.uml.edu/jpropp/reverse.pdf
http://faculty.uml.edu/jpropp/reverse.pdf
Unfolding Finitist Arithmetic
http://math.stanford.edu/~feferman/papers/UnfoldFA.pdf
http://math.stanford.edu/~feferman/papers/UnfoldFA.pdf
The Unfolding of Non-Finitist Airthmetic
http://math.stanford.edu/~feferman/papers/unfolding.pdf
http://math.stanford.edu/~feferman/papers/unfolding.pdf
Believing the Axioms
http://www.cs.umd.edu/~gasarch/BLOGPAPERS/belaxioms1.pdf
http://www.cs.umd.edu/~gasarch/BLOGPAPERS/belaxioms1.pdf
The Strength of Mac Lane Set Theory
https://www.dpmms.cam.ac.uk/~ardm/maclane.pdf
https://www.dpmms.cam.ac.uk/~ardm/maclane.pdf
A Univalent Universe in Finite Order Arithmetic
https://arxiv.org/pdf/1412.6714.pdf
https://arxiv.org/pdf/1412.6714.pdf
Rectangular Axioms, perfect set properties and decomposition
http://www.users.miamioh.edu/larsonpb/goedel.pdf
http://www.users.miamioh.edu/larsonpb/goedel.pdf
Number theory and elementary arithmetic
http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=0F5B8AAA8EBE01A962B6B0DAA8A7A873?doi=10.1.1.105.6509&rep=rep1&type=pdf
http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=0F5B8AAA8EBE01A962B6B0DAA8A7A873?doi=10.1.1.105.6509&rep=rep1&type=pdf
Cardinal Arithmetic in the style of Baron von Münchhausen
https://dspace.library.uu.nl/bitstream/handle/1874/33720/preprint272.pdf?sequence=1&isAllowed=y
https://dspace.library.uu.nl/bitstream/handle/1874/33720/preprint272.pdf?sequence=1&isAllowed=y
Nonstandard Models of Arithmetic
https://diagonalargument.com/mathnotes/nonstandard-models-of-arithmetic-the-series/
https://diagonalargument.com/mathnotes/nonstandard-models-of-arithmetic-the-series/
Diagonal Argument
Nonstandard Models of Arithmetic: The Series
John Baez and I have been conducting a conversation about nonstandard models of Peano arithmetic (PA). This page serves as an annotated table of contents, bibliography, and general repository for s…