A note on rigid substructures
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- by R. J. Parikh PDF
- Proc. Amer. Math. Soc. 33 (1972), 520-522 Request permission
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
- 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
- Hartley Rogers Jr., Theory of recursive functions and effective computability, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1967. MR 0224462
- 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 284323
Additional Information
- © Copyright 1972 American Mathematical Society
- 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