New posts in axioms

Is the Bourbaki treatment of Set Theory outdated?

set-theory axioms

Do we have to prove how parentheses work in the Peano axioms?

logic definition first-order-logic axioms peano-axioms

Why does any transitive model satisfy extensionality?

set-theory axioms

How does the axiom of regularity forbid self containing sets?

elementary-set-theory axioms

What are the consequences if Axiom of Infinity is negated?

analysis set-theory axioms

What's so special about the group axioms?

group-theory soft-question axioms symmetry big-picture

What are disasters with Axiom of Determinacy?

set-theory axioms

Why is "points exist" not an axiom in geometry?

geometry axioms

Is consistency an axiom of mathematics?

set-theory axioms foundations incompleteness

How can I define $\mathbb{N}$ if I postulate existence of a Dedekind-infinite set rather than existence of an inductive set?

set-theory infinity axioms natural-numbers

Proofs given in undergrad degree that need Continuum hypothesis?

soft-question set-theory axioms

Is there a general theory of the "improper" Lebesgue integral?

measure-theory reference-request definition lebesgue-integral axioms

Why does one have to check if axioms are true?

elementary-set-theory logic soft-question axioms foundations

Do these “ultraweak” one-sided group axioms guarantee a group?

abstract-algebra group-theory axioms semigroups

Translating Tarski's Axiomatization/Logic of $\mathbb R$ to the Theory of Magnitudes

real-analysis abstract-algebra logic operator-theory axioms

Why does induction have to be an axiom?

induction axioms peano-axioms

What axioms Gödel is using, if any?

logic axioms incompleteness

Are there infinite sets of axioms?

Can we prove the existence of $A\cup B$ without the union axiom?

set-theory axioms

The existence of the empty set is an axiom of ZFC or not?

set-theory axioms