### Single Idea 17796

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

Full Idea

We can give a semi-categorical axiomatisation of set-theory (all that remains undetermined is the size of the set of urelements and the length of the sequence of ordinals). The system is second-order in formalisation.

Gist of Idea

There is a semi-categorical axiomatisation of set-theory

Source

John Mayberry (What Required for Foundation for Maths? [1994], p.413-2)

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.413

A Reaction

I gather this means the models may not be isomorphic to one another (because they differ in size), but can be shown to isomorphic to some third ingredient. I think. Mayberry says this shows there is no such thing as non-Cantorian set theory.

Related Idea

Idea 17795
Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation **[Mayberry]**