A transfer principle for simple properties of theories
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- by Mark E. Nadel PDF
- Proc. Amer. Math. Soc. 59 (1976), 353-357 Request permission
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
- John Gregory, Uncountable models and infinitary elementary extensions, J. Symbolic Logic 38 (1973), 460–470. MR 376338, DOI 10.2307/2273044
- Mark Nadel, Scott sentences and admissible sets, Ann. Math. Logic 7 (1974), 267–294. MR 384471, DOI 10.1016/0003-4843(74)90017-5
- Mark Nadel, On models $\equiv _{\infty \omega }$ to an uncountable model, Proc. Amer. Math. Soc. 54 (1976), 307–310. MR 392556, DOI 10.1090/S0002-9939-1976-0392556-9 M. Nadel and J. Stavi, The pure part of $\operatorname {hyp} (M)$, J. Symbolic Logic (to appear). J.-P. Ressayre, Models with compactness properties relative to an admissible set (to appear).
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 59 (1976), 353-357
- MSC: Primary 02H10
- DOI: https://doi.org/10.1090/S0002-9939-1976-0414350-2
- MathSciNet review: 0414350