Persistently finite, persistently arithmetic theories

Authors:
C. J. Ash and T. S. Millar

Journal:
Proc. Amer. Math. Soc. **89** (1983), 487-492

MSC:
Primary 03C57; Secondary 03C15, 03C50

DOI:
https://doi.org/10.1090/S0002-9939-1983-0715872-0

MathSciNet review:
715872

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Abstract | References | Similar Articles | Additional Information

Abstract: The main result shows that a certain class of theories, the persistently finite, persistently arithmetic theories, have only arithmetic countable models.

**[M]**Benda,*Remarks on countable models*, Fund. Math.**81**(1974), 107-119. MR**0371634 (51:7852)****[H]**J. Keisler,*Model theory for infinitary logic*, North-Holland, Amsterdam, 1971. MR**0344115 (49:8855)****[T]**S. Millar [1],*Persistently finite theories with hyperarithmetic models*, Trans. Amer. Math. Soc. (to appear). MR**697062 (84m:03053)****[T]**S. Millar [2],*Foundations of recursive model theory*, Ann. Math. Logic**13**(1978), 45-72. MR**482430 (80a:03051)****[M]**G. Peretyat'kin,*Complete theories with a finite number of countable models*, Algebra i Logika**12**(1973), 550-576. MR**0354347 (50:6827)****[J]**G. Rosenstein,*A note on a theorem of Vaught*, J. Symbolic Logic**36**(1971), 439-440. MR**0290950 (45:44)****[R]**L. Vaught,*Denumerable models of complete theories*, Infinitistic Methods (Proc. Sympos. Foundations of Math., Warsaw, 1959), Pergamon, Oxford; PWN, Warsaw, 1961, pp. 303-321. MR**0186552 (32:4011)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1983-0715872-0

Keywords:
Decidable models,
complete types,
hyperarithmetic,
undecidable models

Article copyright:
© Copyright 1983
American Mathematical Society