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A many-sorted interpolation theorem for $ L(Q)$


Author: David R. Guichard
Journal: Proc. Amer. Math. Soc. 80 (1980), 469-474
MSC: Primary 03C75; Secondary 03C80
DOI: https://doi.org/10.1090/S0002-9939-1980-0581007-8
MathSciNet review: 581007
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Abstract: Let L be a many-sorted relational language with $ \in $ and consider the logic $ {L_{{\omega _1}\omega }}(Q)$, infinitary logic with a monotone quantifier. We prove a version of Feferman's Interpolation Theorem for this logic. We then use the theorem to show that for a one-sorted language L and a countable admissible fragment $ {L_A}$ of $ {L_{{\omega _1}\omega }}(Q)$, any sentence which persists for end extensions is equivalent to a $ \Sigma $ sentence.


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

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DOI: https://doi.org/10.1090/S0002-9939-1980-0581007-8
Article copyright: © Copyright 1980 American Mathematical Society

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