Re: Implementable Set Theory and Consistency of ZFC

Jesse F. Hughes wrote:

Here's what I would say. I would say: the empty set is a set with a
particular property, namely that it has no elements. In other words,
when I say the empty set exists, what I mean is that there is a set
with no elements.

Would you say something different?

No.

But I wouldn't say: E x A y - (y in x) , because I want to develop my
set theory without mathematical logic as a prerequisite, and certainly
without needing a specification axiom, like in: x = { y : - (y in x) } .

http://en.wikipedia.org/wiki/Axiom_of_empty_set

Han de Bruijn

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