README.md

Foundations of Mathematics

(Up) | See also: Mathematics, Logic, Incompleteness

Web resources

philosophy of mathematics - What is a natural number? - Philosophy Stack Exchange ★

lo.logic - Most \'unintuitive\' application of the Axiom of Choice? - MathOverflow ★

lo.logic - Why worry about the axiom of choice? - MathOverflow ★

set theory - How much of the axiom of choice do you need in mathematics? - MathOverflow ★

reference request - What can be preserved in mathematics if all constructions are carried out in ZF? - MathOverflow ★

reference request - Lists as a foundation of mathematics - MathOverflow ★

lo.logic - Is there any physical or computational justification for non-constructive axioms such as AC or excluded middle? - MathOverflow ★

lo.logic - Does changing the universe of set theory change the definition of truth? - MathOverflow ★

set theory - Bourbaki\'s definition of the number 1 - MathOverflow ★

The Origin of the Number Zero \| History \| Smithsonian

ct.category theory - How to rewrite mathematics constructively? - MathOverflow ★

How should a \"working mathematician\" think about sets? (ZFC, category theory, urelements) - MathOverflow ★

set theory - Set theories without \"junk\" theorems? - MathOverflow ★

foundations - Why hasn\'t mereology succeeded as an alternative to set theory? - MathOverflow ★

logic - Which is the most powerful language, set theory or category theory? - Mathematics Stack Exchange ★

set theory - Defining the standard model of PA so that a space alien could understand - MathOverflow ★

ULTRAINFINITISM, or a step beyond the transfinite - MathOverflow ★

Set-theoretical multiverse and foundations - MathOverflow ★

New Foundations and weaker forms of choice - MathOverflow ★

getting rid of existential quantifiers - MathOverflow ★

Paris--Harrington theorem - Wikipedia, the free encyclopedia

lo.logic - What sorts of extra axioms might we add to ZFC to compute higher Busy Beaver numbers? - MathOverflow ★

set theory - Are there first-order statements that second order PA proves that first order PA does not? - MathOverflow ★

(in Type Theory) Type Theory and Mathematical Logic \| artagnon.com ★

Books

(in Logic) Mathematical Logic (Kleene) (borrow @ archive.org) 🏛️ 💭

(in Mathematics) Compactness and Contradiction (online @ terrytao.wordpress.com)