How is it possible that the well-ordering theorem is strictly stronger than the axiom of choice in second-order logic?
114550
Well-ordering theorem and second-order logic
141814
Proofs using theorems instead of axioms
96504
First-Order Logic vs. Second-Order Logic
12539
Set Theory: Equivalency of Axiom of Choice and Choice Function
45623
Axiom of Choice: What exactly is a choice, and when and why is it needed?
578
In classical logic, why is $(p\Rightarrow q)$ True if both $p$ and $q$ are False?
62936
Proving equivalencies of two versions of the Axiom of Choice
25567
Is there any significance in the order in which group axioms are presented?
82739
Why is $\alpha \rightarrow \forall x(\alpha)$ not generally correct in first-order logic?
132287
Axiom of Choice and Right Inverse
150385
The use of the Axiom of Choice in this proof of the sequence lemma
45878
Elementary Set Theory: Ordinals, Well Orderings and Isomorphisms
69337
Zorn's Lemma And Axiom of Choice
149277
Does well-ordering of the proper class of cardinal numbers imply choice?
131889
Axiom of choice and calculus
83757
Is the following equivalent to the axiom of choice?
50506
What concept does an open set axiomatise?