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×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×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)