amazingly simple set theory

[juan_gandhi]

Pocket Set Theory 

PST also verifies the:

• Continuum hypothesis. This follows from (5) and (6) above;
• Axiom of replacement. This is a consequence of (A4);
• Axiom of choice. Proof. The class Ord of all ordinals is well-ordered by definition. Ord and the class V of all sets are both proper classes, because of the Burali-Forti paradox and Cantor's paradox, respectively. Therefore there exists a bijection between V and Ord, which well-orders V. ∎

The well-foundedness of all sets is neither provable nor disprovable in PST.