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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
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?)

  • [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,
  • [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,

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