Foundations of Mathematics

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

Works regarding the foundations of mathematics, including systems in which doing mathematics is possible, and the philosophical underpinnings of mathematics.

Web resources

What is a natural number? ★

Most \'unintuitive\' application of the Axiom of Choice? ★

Why worry about the axiom of choice? ★

How much of the axiom of choice do you need in mathematics? ★

What can be preserved in mathematics if all constructions are carried out in ZF? ★

Lists as a foundation of mathematics ★

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

Does changing the universe of set theory change the definition of truth? ★

Bourbaki\'s definition of the number 1 ★

The Origin of the Number Zero | History | Smithsonian

How to rewrite mathematics constructively? ★

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

Set theories without \"junk\" theorems? ★

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

Which is the most powerful language, set theory or category theory? ★

Defining the standard model of PA so that a space alien could understand ★

ULTRAINFINITISM, or a step beyond the transfinite ★

Set-theoretical multiverse and foundations ★

New Foundations and weaker forms of choice ★

getting rid of existential quantifiers ★

Paris--Harrington theorem - Wikipedia, the free encyclopedia

What sorts of extra axioms might we add to ZFC to compute higher Busy Beaver numbers? ★

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

(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)