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A transfer principle for simple properties of theories

Author: Mark E. Nadel
Journal: Proc. Amer. Math. Soc. 59 (1976), 353-357
MSC: Primary 02H10
MathSciNet review: 0414350
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Abstract: A notion of simple property of theories is introduced and it is shown that if $ {\text{P}}$ is a simple property of theories, $ A$ countable admissible, and $ M$ a structure in $ A$, then $ {\operatorname{Th} _A}(M)$ has property $ {\text{P}}$ iff $ {\operatorname{Th} _{\infty \omega }}(M)$ has property $ {\text{P}}$.

References [Enhancements On Off] (What's this?)

  • [1] J. Gregory, Uncountable models and infinitary extensions, J. Symbolic Logic 38 (1973), 460-470. MR 0376338 (51:12514)
  • [2] M. Nadel, Scott sentences and admissible sets, Ann. Math. Logic 7 (1974), 267-294. MR 0384471 (52:5348)
  • [3] -, On models $ { \equiv _{\infty \omega }}$ to an uncountable model, Proc. Amer. Math. Soc. 54 (1976), 307-310. MR 0392556 (52:13373)
  • [4] M. Nadel and J. Stavi, The pure part of $ \operatorname{hyp} (M)$, J. Symbolic Logic (to appear).
  • [5] J.-P. Ressayre, Models with compactness properties relative to an admissible set (to appear).

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