FOM: How not to use universes, queries

[Kanovei]

From: cxm7 at po.cwru.edu (Colin McLarty)
Date: Sat, 10 Apr 1999 15:28:30 -0400 (EDT)
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Say a "Grothendieck weak-universe" is a transitive set U which
models ZFC except for replacement, and further every subset of an element of
U is also an element of U. 

        Is ZFC+(a weak-universe) really a weaker theory that ZFC+(a
universe) or does the strength of ZFC make extension by a weak-universe
equivalent to extension by a universe?
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In ZFC, if a is a limit ordinal then V_a is a 
"Grothendieck weak-universe" in that sense. 
So, ZFC+(a weak-universe)=ZFC.