User:Asalmon
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The list on here previously is now largely out of date.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 $\S 1 - \S 9$. Basis Representation Theorem for Ordinals is just proven. $\S 9$ is done! Skipped Well-Founded Recursion, though. May come back to it later.
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.
Template for me...
eqn with "ll"
| \(\ds \) | \(\) | \(\ds \) | ||||||||||||
| \(\ds \) | \(\) | \(\ds \) | ||||||||||||
| \(\ds \) | \(\) | \(\ds \) |
eqn with equality
| \(\ds \) | \(=\) | \(\ds \) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \) |
eqn template
| \(\ds \) | \(\implies\) | \(\ds \) | ||||||||||||
| \(\ds \) | \(\implies\) | \(\ds \) | ||||||||||||
| \(\ds \) | \(\implies\) | \(\ds \) | ||||||||||||
| \(\ds \) | \(\implies\) | \(\ds \) |
Proofs by Transfinite Induction Template
The proof shall proceed by Transfinite Induction on $$.
Basis for the Induction
This proves the basis for the induction.
$\Box$
Induction Step
This proves the induction step.
$\Box$
Limit Case
This proves the limit case.
$\blacksquare$
Sources
- 1971: Gaisi Takeuti and Wilson M. Zaring: Introduction to Axiomatic Set Theory: $\S $