TY - JOUR
T1 - A hanf number for saturation and omission
T2 - The superstable case
AU - Baldwin, John T.
AU - Shelah, Saharon
N1 - Publisher Copyright:
© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
PY - 2014/11/1
Y1 - 2014/11/1
N2 - Suppose t=(T,T1,p) is a triple of two theories in vocabularies τ⊂τ1 with cardinality λ, T⊆T1 and a τ1-type p over the empty set that is consistent with T1. We consider the Hanf number for the property "there is a model M1 of T1 which omits p, but M1{up harpoon right}τ is saturated". In [2], we showed that this Hanf number is essentially equal to the Löwenheim number of second order logic. In this paper, we show that if T is superstable, then the Hanf number is less than Beth{hebrew}(2(2λ)+)+.
AB - Suppose t=(T,T1,p) is a triple of two theories in vocabularies τ⊂τ1 with cardinality λ, T⊆T1 and a τ1-type p over the empty set that is consistent with T1. We consider the Hanf number for the property "there is a model M1 of T1 which omits p, but M1{up harpoon right}τ is saturated". In [2], we showed that this Hanf number is essentially equal to the Löwenheim number of second order logic. In this paper, we show that if T is superstable, then the Hanf number is less than Beth{hebrew}(2(2λ)+)+.
UR - http://www.scopus.com/inward/record.url?scp=84911480494&partnerID=8YFLogxK
U2 - 10.1002/malq.201300022
DO - 10.1002/malq.201300022
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AN - SCOPUS:84911480494
SN - 0942-5616
VL - 60
SP - 437
EP - 443
JO - Mathematical Logic Quarterly
JF - Mathematical Logic Quarterly
IS - 6
ER -