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. An approach to definability theory*, Perspectives in Mathematical Logic, Springer-Verlag, Berlin-New York, 1975. MR**0424560 (54:12519)****[2]**-,*Monotone quantifiers and admissible sets*, Generalized Recursion Theory. II, North-Holland, Amsterdam, 1978. MR**516928 (81d:03037)****[3]**Kim Bruce,*Ideal models and some not so ideal problems in the model theory of*, J. Symbolic Logic**43**(1978), 304-321. MR**499380 (80a:03048)****[4]**Solomon Feferman,*Applications of many-sorted interpolation theorems*, Proceedings of the Tarski Symposium, (Proc. Sympos. Pure Math., vol. 25, Univ. of California, Berkeley, 1971), Amer. Math. Soc., Providence, R.I., 1974, pp. 205-223. MR**0406772 (53:10558)****[5]**H. J. Keisler,*Model theory for infinitary logic*, North-Holland, Amsterdam, 1971.**[6]**Bienvenido F. Nebres,*Infinitary formulas preserved under unions*, J. Symbolic Logic**37**(1972), 449. MR**0403915 (53:7724)**

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

Article copyright:
© Copyright 1980
American Mathematical Society