A many-sorted interpolation theorem for

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 and consider the logic , 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 of , any sentence which persists for end extensions is equivalent to a sentence.

**[1]**Jon Barwise,*Admissible sets and structures*, Springer-Verlag, Berlin-New York, 1975. An approach to definability theory; Perspectives in Mathematical Logic. MR**0424560****[2]**Jon Barwise,*Monotone quantifiers and admissible sets*, Generalized recursion theory, II (Proc. Second Sympos., Univ. Oslo, Oslo, 1977) Stud. Logic Foundations Math., vol. 94, North-Holland, Amsterdam-New York, 1978, pp. 1–38. MR**516928****[3]**Kim B. Bruce,*Ideal models and some not so ideal problems in the model theory of 𝐿(𝑄)*, J. Symbolic Logic**43**(1978), no. 2, 304–321. MR**499380**, https://doi.org/10.2307/2272829**[4]**Solomon Feferman,*Applications of many-sorted interpolation theorems*, Proceedings of the Tarski Symposium (Proc. Sympos. Pure Math., Vol. XXV, Univ. of California, Berkeley, Calif., 1971) Amer. Math. Soc., Providence, R. I., 1974, pp. 205–223. MR**0406772****[5]**H. J. Keisler,*Model theory for infinitary logic*, North-Holland, Amsterdam, 1971.**[6]**Bienvenido F. Nebres,*Infinitary formulas preserved under unions of models*, J. Symbolic Logic**37**(1972), 449–465. MR**0403915**, https://doi.org/10.2307/2272730

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DOI:
https://doi.org/10.1090/S0002-9939-1980-0581007-8

Article copyright:
© Copyright 1980
American Mathematical Society