A Hanf number for saturation and omission: the superstable case | Zendy

Baldwin John T. | Zendy; Shelah Saharon | Zendy

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A Hanf number for saturation and omission: the superstable case

Author(s) -

Baldwin John T.,

Shelah Saharon

Publication year - 2014

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.201300022

Subject(s) - mathematics , cardinality (data modeling) , combinatorics , saturation (graph theory) , set (abstract data type) , discrete mathematics , computer science , data mining , programming language

Suppose t = ( T , T 1 , p ) is a triple of two theories in vocabularies τ ⊂ τ 1with cardinality λ, T ⊆ T 1and a τ 1 ‐type p over the empty set that is consistent with T 1 . We consider the Hanf number for the property “there is a model M 1 of T 1 which omits p , butM 1 ↾ 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 ℶ ( 2 ( 2 λ ) + )+.

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