more from David Bostock

### Single Idea 18115

#### [catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets]

Full Idea

We could add the axiom that all sets are constructible (V = L), making the universe of sets as small as possible, or add the axiom that there is a supercompact cardinal (SC), making the universe as large as we no know how to.

Gist of Idea

We could add axioms to make sets either as small or as large as possible

Source

David Bostock (Philosophy of Mathematics [2009], 6.4)

Book Reference

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.188

A Reaction

Bostock says most mathematicians reject the first option, and are undecided about the second option.