Vol. 36, No. 3, 1971

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On the number of non-almost isomorphic models of T in a power

Saharon Shelah

Vol. 36 (1971), No. 3, 811–818
Abstract

Let T be a first order theory. Two models are almost isomorphic if they are elementarily equivalent in the language L. We investigate the number of non almost-isomorphic models of T of power λ as a function of λ,I(T,λ). We prove μ > λ |T|,I(T,λ) λ implies I(T,μ) I(T,λ). In fact, we generalize the downward Skolem-Lowenheim theorem for infinitary languages. Th. (1, 4, 5).

Mathematical Subject Classification
Primary: 02.50
Milestones
Received: 19 August 1969
Published: 1 March 1971
Authors
Saharon Shelah