How does the Axiom of Foundation prevent an infinitely descending membership sequence?
109926
Axiom of Regularity and infinite sequences
36626
Multiplication cancellation property by Peano axioms
950
Doubts on the axiom of union?
105815
Does proving (second countable) $\Rightarrow$ (Lindelöf) require the axiom of choice?
109054
Given an infinite set of cardinality $X$, is there a chain in $\mathcal P(X)$ of the same cardinalty of $\mathcal P(X)$?
102490
Does this recursive sequence have a closed-form?
119624
A Dedekind infinite set has a countably infinite proper subset
84485
What is the purpose of the Axiom of regularity/foundation?
35123
How do the separation axioms follow from the replacement axioms?
23076
Proof of limit of quotient sequence property
108533
Is there any formula of monadic second-order logic that is only satisfied by an infinite set?
146560
Is there any uncountably infinite set that does not generate the reals?
85398
$\mathsf{ZF}$ is not finitely axiomatizable
143146
Help with completing the proof: Any unbounded sequence is either infinitely large or has a convergent subsequential limit
117561
A set is infinite iff there is a one-to-one correspondent with one of its proper subsets?
60678
Does 'A countable infinite Cartesian product of countable sets is not necessarily countable' violate induction principle?
31389
consistency of ZF\{Power Set axiom}