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A note on rigid substructures

Author: R. J. Parikh
Journal: Proc. Amer. Math. Soc. 33 (1972), 520-522
MSC: Primary 02H99
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, especially p. 193. MR 33 #7257. MR 0199107 (33:7257)
  • [2] H. Rogers, Jr., Theory of recursive functions and effective computability, McGraw-Hill, New York, 1967. MR 37 #61. MR 0224462 (37:61)
  • [3] F. Ville, Complexité des structures rigidement contenues dans une théorie du premier ordre, C. R. Acad. Sci. Paris Sér. A 272 (1971), 561-563. MR 0284323 (44:1552)

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Keywords: Rigid substructures, recursive theory
Article copyright: © Copyright 1972 American Mathematical Society

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