TY - JOUR
T1 - A dependent theory with few indiscernibles
AU - Kaplan, Itay
AU - Shelah, Saharon
N1 - Publisher Copyright:
© 2014, Hebrew University of Jerusalem.
PY - 2014/10/2
Y1 - 2014/10/2
N2 - We give a full solution to the question of existence of indiscernibles in dependent theories by proving the following theorem: For every θ there is a dependent theory T of size θ such that for all κ and δ, κ → (δ)T,1iff κ → (δ)θ <ω. This means that unless there are good set theoretical reasons, there are large sets with no indiscernible sequences.
AB - We give a full solution to the question of existence of indiscernibles in dependent theories by proving the following theorem: For every θ there is a dependent theory T of size θ such that for all κ and δ, κ → (δ)T,1iff κ → (δ)θ <ω. This means that unless there are good set theoretical reasons, there are large sets with no indiscernible sequences.
UR - http://www.scopus.com/inward/record.url?scp=84908509256&partnerID=8YFLogxK
U2 - 10.1007/s11856-014-1067-2
DO - 10.1007/s11856-014-1067-2
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AN - SCOPUS:84908509256
SN - 0021-2172
VL - 202
SP - 59
EP - 103
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -