Why is the "axiom of extension" an axiom?
40291
What's the point of the axiom of extensionality?
49276
Why don't you need the Axiom of Choice when constructing the "inverse" of an injection?
58447
Is axiom of choice required for there to be an infinite linearly independent set in a (non-finite-dimensional) vector space?
96355
What is the first order axiom characterizing a field having characteristic zero?
13661
Axiom of Regularity allows for this set be an element of itself
66636
Problems with introducing ordered pairs axiomatically
78148
Why does the infinite prisoners and hats puzzle require the axiom of choice?
131889
Axiom of choice and calculus
115675
Strange consequences of Axiom of Choice in Zermelo set theory
84562
Proof using only field axioms
31509
Is axiom of choice necessary for proving that every infinite set has a countably infinite subset?
55564
Can the union axiom be weakened?
31212
The existence of the empty set is an axiom of ZFC or not?
77654
Is the uncertainty principle axiomatic or derived?
49682
What axiomatizations exist for special relativity?
12272
Why $a$ is not an essential singularity and how $f$ can be extended
109926
Axiom of Regularity and infinite sequences