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The list on here previously is now largely out of date.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 $\S 7$. The next chapter is on ordinal arithmetic. I will get tired of transfinite induction. Unique Representation of Ordinal as Sum is just proven. Different from the proof given in the book (it's shorter).

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.