A hanf number for saturation and omission: The superstable case

John T. Baldwin; Saharon Shelah

doi:10.1002/malq.201300022

A hanf number for saturation and omission: The superstable case

John T. Baldwin^*
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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)+)+.

Original language	English
Pages (from-to)	437-443
Number of pages	7
Journal	Mathematical Logic Quarterly
Volume	60
Issue number	6
DOIs	https://doi.org/10.1002/malq.201300022
State	Published - 1 Nov 2014

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© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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title = "A hanf number for saturation and omission: The superstable case",

abstract = "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 L{\"o}wenheim 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)+)+.",

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A hanf number for saturation and omission: The superstable case

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