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Topic: Two Grothendieck universes
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William Elliot

Posts: 2,383
Registered: 1/8/12
Two Grothendieck universes
Posted: May 13, 2014 10:52 AM
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Wikipedia Definition
G Grothendieck universe when for all A,B in G,
> { A,B }, P(A) in G,  A subset B  and
> for all J in G, (for all j in J, Aj in G ==> \/_j Aj in G)

Victor Porton Definition
G Grothendieck universe when for all A,B in G,
> { A,B }, P(A), \/A in G,  A subset G

Are the two definitions equivalent?
Clearly a Wikipedia Grothendieck universe
is a Victor Porton Grothendieck universe,
simply because \/C = \/{ A | A in C }.

Does the converse hold?  Within a Victor Porton universe, if
A in G, f:A -> G and for all a in A, f(a) in G, is f(A) in G?

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