Talk:Code (set theory)

Latest comment: 16 years ago by YohanN7 in topic A definition easier to follow

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)Reply