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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A two-cardinal theorem


Author: Saharon Shelah
Journal: Proc. Amer. Math. Soc. 48 (1975), 207-213
DOI: https://doi.org/10.1090/S0002-9939-1975-0357105-9
MathSciNet review: 0357105
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Abstract | References | Additional Information

Abstract: We prove the following theorem and deal with some related questions: If for all $ n < \omega ,T$ has a model $ M$ such that $ {n^n} \leq \vert{Q^M}{\vert^n} \leq \vert{P^M}\vert < {\aleph _0}$ then for all $ \lambda ,\mu $ such that $ \vert T\vert \leq \mu \leq \lambda < {\operatorname{Ded} ^ \ast }(\mu )$ (e.g. $ \mu = {\aleph _0},\lambda = {2^{{\aleph _0}}}), T$ has a model of type $ (\lambda ,\mu )$, i.e. $ \vert{Q^M}\vert = \mu ,\vert{P^M}\vert = \lambda $.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0357105-9
Keywords: Two-cardinal theorem, finite models
Article copyright: © Copyright 1975 American Mathematical Society