more from Robert S. Wolf

Single Idea 13529

[catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / e. Axiom of the Empty Set IV]

Full Idea

Empty Set Axiom: ∃x ∀y (y ∈ x). There is a set x which has no members (no y's). The empty set exists. There is a set with no members, and by extensionality this set is unique.

Gist of Idea

Empty Set: ∃x∀y (y∈x). The unique empty set exists

Source

Robert S. Wolf (A Tour through Mathematical Logic [2005], 2.3)

Book Reference

Wolf,Robert S.: 'A Tour Through Mathematical Logic' [Carus Maths Monographs 2005], p.70


A Reaction

A bit bewildering for novices. It says there is a box with nothing in it, or a pair of curly brackets with nothing between them. It seems to be the key idea in set theory, because it asserts the idea of a set over and above any possible members.