User:Asalmon

The list on here previously is now largely out of date. Use the list on the book page for Introduction to Axiomatic Set Theory.

I have now finished all the proofs in $\S 1 - \S 8$. Basis Representation Theorem for Ordinals is just proven. Different from the proof given in the book (it's shorter). Well-Founded Recursion is a pain. It's basically the same proof as Transfinite Recursion.

Judging by the length of the proof, I expect Sierpinski's proof that $\operatorname{GCH} \implies \operatorname{AC}$ to break the record for page length on this site, even excluding the lemmas.

Template for me...

Proofs by Transfinite Induction Template
The proof shall proceed by Transfinite Induction on $$.

Basis for the Induction
This proves the basis for the induction.

Induction Step
This proves the induction step.

Limit Case
This proves the limit case.