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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A note on rigid substructures


Author: R. J. Parikh
Journal: Proc. Amer. Math. Soc. 33 (1972), 520-522
MSC: Primary 02H99
DOI: https://doi.org/10.1090/S0002-9939-1972-0294112-6
MathSciNet review: 0294112
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Abstract: We show that a theory with a recursive set of axioms may have (nontrivial) rigid substructures and yet fail to have $ \Sigma _1^1$, or $ \Pi _1^1$ rigid substructures.


References [Enhancements On Off] (What's this?)

  • [1] G. Kreisel, Model-theoretic invariants: Applications to recursive and hyperarithmetic operations, Theory of Models (Proc. 1963 Internat. Sympos. Berkeley), North-Holland, Amsterdam, 1965, pp. 190–205. MR 0199107
  • [2] Hartley Rogers Jr., Theory of recursive functions and effective computability, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1967. MR 0224462
  • [3] Françoise Ville, Complexité des structures rigidement contenues dans une théorie du premier ordre, C. R. Acad. Sci. Paris Sér. A-B 272 (1971), A561–A563 (French). MR 0284323

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0294112-6
Keywords: Rigid substructures, recursive theory
Article copyright: © Copyright 1972 American Mathematical Society