Single Idea 13029

[catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence]

Full Idea

Axiom of Set Existence: ∃x (x = x). This says our universe is non-void. Under most developments of formal logic, this is derivable from the logical axioms and thus redundant, but we do so for emphasis.

Gist of Idea

Set Existence: ∃x (x = x)

Source

Kenneth Kunen (Set Theory [1980], §1.5)

Book Reference

Kunen,Kenneth: 'Set Theory: Introduction to Independence Proofs' [North-Holland 1980], p.10