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On the number of
non-almost isomorphic models of T in a power
Saharon Shelah |
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Vol. 36 (1971), No. 3, 811–818
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Abstract |
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Let T be a first order theory. Two models are almost isomorphic if they are elementarily equivalent in the language L∞,ω. 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
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Milestones
Received: 19 August 1969
Published: 1 March 1971
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Authors |
| Saharon Shelah | |
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