Talk:Code (set theory)

A definition easier to follow
There is probably nothing wrong in the article as it stands, but I want to change the beginning of it anyway. The reason is that I don't like when (for most people) nontrivial concepts are introduced in a single sentence and, in addition, the notation is introduced in nested "where-clauses" and "such-that-clauses" I'll replace
 * In set theory, a code for a set


 * x $$\in H_{\aleph_1},$$


 * the notation standing for the hereditarily countable sets,


 * is a set


 * E $$\subset$$ ω&times;ω


 * such that there is an isomorphism between (ω,E) and (X,$$\in$$) where X is the transitive closure of {x}.

with this
 * In set theory a code of a set is defined as follows. Let $$x$$ be a hereditarily countable set, and let $$X$$ be the transitive closure of $$\{x\}$$. Let as usual $$\omega$$ denote the set of natural numbers and let $$\aleph_1$$ be the first uncountable cardinal number. In this notation we have $$x \in H_{\aleph_1}$$. Also recall that $$(X,\in)$$ denotes the relation of belonging in $$X$$.
 * A code for $$x$$ is any set $$E$$ satisfying the following two properties:
 * 1.) $$E$$ $$\subset$$ ω&times;ω
 * 2.) There is an isomorphism between $$(\omega,E)$$ and $$(X,\in)$$.

if there are no objections.

YohanN7 (talk) 23:13, 6 June 2008 (UTC)