Nice name
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A nice name is a set theoretical concept used in forcing to impose an upper bound on the number of subsets in the generic model. It is a technical concept used in the context of forcing to prove independence results in set theory such as Easton's theorem.
[edit] Formal Definition
Let 
ZFC be transitive, 
a forcing notion in M, and suppose 
is generic over M. Then for any 
-name in M, τ,
η is a nice name for a subset of τ if η is a -name satisfying the following properties:
(1) 
(2) For all -names 
, 
forms an antichain.
(3) (Natural Addition): If 
, then there exists 
in such that 
.
