Tame theories with hyperarithmetic homogeneous models
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- by Terrence Millar PDF
- Proc. Amer. Math. Soc. 105 (1989), 712-726 Request permission
Abstract:
A tame theory is a decidable first-order theory with only countably many countable models, and all complete types recursive. It is shown here that the recursive complexity of countable homogeneous models of tame theories is unbounded in the hyperarithmetic hierarchy.References
- Terrence S. Millar, Foundations of recursive model theory, Ann. Math. Logic 13 (1978), no. 1, 45–72. MR 482430, DOI 10.1016/0003-4843(78)90030-X
- Terrence Millar, Decidability and the number of countable models, Ann. Pure Appl. Logic 27 (1984), no. 2, 137–153. MR 763737, DOI 10.1016/0168-0072(84)90009-5
- T. S. Millar, Type structure complexity and decidability, Trans. Amer. Math. Soc. 271 (1982), no. 1, 73–81. MR 648078, DOI 10.1090/S0002-9947-1982-0648078-8
- Terry Millar, Bad models in nice neighborhoods, J. Symbolic Logic 51 (1986), no. 4, 1043–1055. MR 865930, DOI 10.2307/2273916
- Hartley Rogers Jr., Theory of recursive functions and effective computability, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1967. MR 0224462
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 105 (1989), 712-726
- MSC: Primary 03C57; Secondary 03C50
- DOI: https://doi.org/10.1090/S0002-9939-1989-0937851-6
- MathSciNet review: 937851