New posts in axioms

Axiomatic characterization of the rational numbers

logic field-theory axioms rational-numbers

Interesting examples of first-order, one-sorted proper extensions of PA

logic first-order-logic axioms natural-numbers peano-axioms

Axiom of extensionality in ZF - pointless?

set-theory axioms

What are natural numbers?

logic set-theory philosophy axioms

Axiomatic definition of sin and cos?

trigonometry axioms

Where is axiom of regularity actually used?

set-theory axioms

Axiom of Regularity

set-theory axioms

Meaning of the word "axiom"

logic axioms philosophy

Is every axiom in the definition of a vector space necessary?

abstract-algebra vector-spaces definition axioms

Can proof by contradiction 'fail'?

logic soft-question axioms foundations proof-theory

Axiomatic approach to polynomials?

abstract-algebra polynomials axioms

How do the separation axioms follow from the replacement axioms?

elementary-set-theory axioms

What is the modern axiomatization of (Euclidean) plane geometry?

geometry reference-request euclidean-geometry axioms

How does (ZFC-Infinity+"There is no infinite set") compare with PA?

logic set-theory axioms peano-axioms

Is $\{0\}$ a field?

field-theory axioms

What is exactly the difference between a definition and an axiom?

terminology definition axioms proof-theory

Has there ever been an application of dividing by $0$?

divisibility axioms

Is there a succinct way to axiomatize the theory of a single elementary topos?

logic category-theory axioms topos-theory

Does mathematics require axioms?

logic soft-question philosophy axioms foundations

In what sense are math axioms true?

logic philosophy axioms