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Two Grothendieck universes
Posted:
May 13, 2014 10:52 AM


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?



