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A Determinate Logic

Published online by Cambridge University Press:  22 January 2016

Gaisi Takeuti
Gaisi Takeuti*
Affiliation:
University of Illinois
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Let L be a fixed language and K be a set of structures related to L. A sentence in L is said to be K-valid if and only if for every structure in K,

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 38 , March 1970 , pp. 113 - 138
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

[1] Gale, D. and Stewart, F., Infinite games with perfect information, Annals of Mathematics Study No. 28, Princeton, 1953, pp. 245–266.Google Scholar
[2] Henkin, L., Some remarks on infinitely long formulas. Infinitistic Methods, pp. 167–183, Warszawa 1961.Google Scholar
[3] Maehara, S. and Takeuti, G., A formal system of first order predicate calculus with infinitely long expressions, J. Math. Soc. Japan 13 (1961), pp. 357–370.Google Scholar
[4] Malitz, J., Problems in the Model Theory of Infinite Languages. Ph. D. Thesis, Berkeley, 1966.Google Scholar
[5] Mycielski, J., On the Axiom of Determinateness, Fundamenta Mathematicae 53 (1964), pp. 205–224.CrossRefGoogle Scholar
[6] Mycielski, J. and Steinhaus, H., A mathematical axiom contradicting the axiom of choice, Bull. Pol. Acad. 10 (1962), p. 1.Google Scholar