TY - JOUR
T1 - More on regular reduced products
AU - Kennedy, Juliette Cara
AU - Shelah, Saharon
PY - 2004/12
Y1 - 2004/12
N2 - The authors show, by means of a finitary version □ λ.Dfin of the combinatorial principle □λb* of [7]. the consistency of the failure, relative to the consistency of supercompact cardinals, of the following: for all regular filters D on a cardinal λ, if Mi and Ni are elementarily equivalent models of a language of size <λ, then the second player has a winning strategy in the Ehrenfeucht-Fraïssé game of length λ+ on ∏i Mi/D and ∏i Ni/D. If in addition 2λ = λ+ and i < λ implies |Mi| + |Ni| ≤ λ+ this means that the ultrapowers are isomorphic. This settles negatively conjecture 18 in [2].
AB - The authors show, by means of a finitary version □ λ.Dfin of the combinatorial principle □λb* of [7]. the consistency of the failure, relative to the consistency of supercompact cardinals, of the following: for all regular filters D on a cardinal λ, if Mi and Ni are elementarily equivalent models of a language of size <λ, then the second player has a winning strategy in the Ehrenfeucht-Fraïssé game of length λ+ on ∏i Mi/D and ∏i Ni/D. If in addition 2λ = λ+ and i < λ implies |Mi| + |Ni| ≤ λ+ this means that the ultrapowers are isomorphic. This settles negatively conjecture 18 in [2].
UR - http://www.scopus.com/inward/record.url?scp=11844253205&partnerID=8YFLogxK
U2 - 10.2178/jsl/1102022222
DO - 10.2178/jsl/1102022222
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AN - SCOPUS:11844253205
SN - 0022-4812
VL - 69
SP - 1261
EP - 1266
JO - Journal of Symbolic Logic
JF - Journal of Symbolic Logic
IS - 4
ER -