Talk:Code (set theory)

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 Field:  Foundations, logic, and set theory

A definition easier to follow[edit]

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
the notation standing for the hereditarily countable sets,
is a set
E ω×ω
such that there is an isomorphism between (ω,E) and (X,) where X is the transitive closure of {x}.

with this

In set theory a code of a set is defined as follows. Let be a hereditarily countable set, and let be the transitive closure of . Let as usual denote the set of natural numbers and let be the first uncountable cardinal number. In this notation we have . Also recall that denotes the relation of belonging in .
A code for is any set satisfying the following two properties:
1.) ω×ω
2.) There is an isomorphism between and .

if there are no objections.

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