The Universe of Discourse

Sun, 23 Jan 2022

Annoying mathematical notation

Recently I've been thinking that maybe the thing I really dislike about set theory might the power set axiom. I need to do a lot more research about this, so any blog articles about it will be in the distant future. But while looking into it I ran across an example of a mathematical notation that annoyed me.

This paper of Gitman, Hamkins, and Johnstone considers a subtheory of ZFC, which they call “!!ZFC-!!”, obtained by omitting the power set axiom. Fine so far. But the main point of the paper:

Nevertheless, these deficits of !!ZFC-!! are completely repaired by strengthening it to the theory !!ZFC^−!!, obtained by using collection rather than replacement in the axiomatization above.

Got that? They are comparing two theories that they call “!!ZFC-!!” and “!!ZFC^-!!”.

(Blog post by Gitman (archived))

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