How do I prove that the sets x = {y}, y = {z} and z = {x} can’t exist with the axiom of regulation/foundation in ZFC?
7865
Complete Newbie: Axiom of Foundation Exercise
42095
Existence in ZF of a set with countable power set
104550
Countable union of countable sets(ZF)
27899
Can we prove the existence of $A\cup B$ without the union axiom?
61747
Proof of exchange principle in set theory
119982
how to express the set of natural numbers in ZFC
122184
De Morgan's laws in logic and set theory
135957
Why in an inconsistent axiom system every statement is true? (For Dummies)
127362
How do I prove that there doesn't exist a set whose power set is countable?
107383
Derived sets - prove $(A \cup B)' = A' \cup B'$
141299
Alternative set theories
18484
Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.
146188
Why does a proof of $\exists f: X\to Y$ injection $\iff \exists g: Y \to X$ surjection requires the axiom of choice?
139992
Is power-associativity finitely axiomatizable?
5313
Existence of how many sets is asserted by the axiom of choice in this case?
29755
Power set equivalency of Axiom of Choice
28452
Statement that is provable in $ZFC+CH$ yet unprovable in $ZFC+\lnot CH$