https://snowlesswinter.neocities.org/tags/jech/ Recent content in jech on snowlesswinter.com Hugo -- gohugo.io en-us Wed, 16 Mar 2022 12:42:07 -0600 https://snowlesswinter.neocities.org/posts/classes/ Wed, 16 Mar 2022 12:42:07 -0600 https://snowlesswinter.neocities.org/posts/classes/ Our last post took us through the axioms of ZF and explored the first two in detail. This post explores the schema of separation and the notion of classes in ZF. Schema of separation Recall that the fourth axiom of ZF is the schema of separation, which states that if $P$ is a predicate with parameter $p$, then for any $X$ and $p$ there exists a set $Y = \{u \in X \mid P(u,p) \}$. https://snowlesswinter.neocities.org/posts/jech1/ Sat, 26 Feb 2022 00:00:00 +0000 https://snowlesswinter.neocities.org/posts/jech1/ Introduction Set theoretic ideas were banging around the mathematical world for a long time, but Georg Cantor and Richard Dedekind are usually credited as the pro- genitors of what we call naïve set theory. Naïve set theory doesn’t refer to one theory but rather to a collection of informal, natural language descriptions of set theory. It wasn’t long after these descriptions emerged that fundamental problems inherent in them–including but not limited to famous Russell’s paradox–also emerged.