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On the model theory of denumerably long formulas with finite strings of quantifiers

Published online by Cambridge University Press:  12 March 2014

M. Makkai
M. Makkai*
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences, Budapest
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Extract

In this paper we prove infinitary analogues of model-theoretic results known for finitary logic. The infinitary language we deal with is Lω1ω which is roughly described by saying that, in addition to the usual formation rules of the lower predicate calculus with identity, also the formation of the conjunction and disjunction of countably many formulas is allowed.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 34 , Issue 3 , 17 November 1969 , pp. 437 - 459
Copyright
Copyright © Association for Symbolic Logic 1969

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References

[1]Barwise, J., Infinitary logic and admissible sets, Doctoral Dissertation, Stanford University, Stanford, Calif., 1967.Google Scholar
[2]Barwise, J., Remarks on universal sentences of Lω1ω (to appear).Google Scholar
[3]Barwise, J., Infinitary logic and admissible sets, this Journal, vol. 34 (1969), pp. 226–252.Google Scholar
[4]Feferman, S., Persistent and invariant formulas for outer extension, this Journal, vol. 34 (1969) (to appear).Google Scholar
[5]Feferman, S. and Kreisel, G., Persistent and invariant formulas relative to theories of higher order, Bulletin of the American Mathematical Society, vol. 72 (1966), pp. 480–485.CrossRefGoogle Scholar
[6]Henkin, L. A., An extension of the Craig-Lyndon interpolation theorem, this Journal, vol. 28 (1963), pp. 201–216.Google Scholar
[7]Karp, C. R., Languages with expressions of infinite length, North-Holland, Amsterdam, 1964.Google Scholar
[8]Keisler, H. J., Some applications of infinitely long formulas, this Journal, vol. 30 (1965), pp. 339–349.Google Scholar
[9]Lopez-Escobar, E. G. K., An interpohtion theorem for denumerably long formulas, Fundamenta mathematicae, vol. 57 (1965), pp. 253–272.CrossRefGoogle Scholar
[10]Los, J., On extending of models. I, Fundamenta mathematicae, vol. 42 (1955), pp. 38–54.CrossRefGoogle Scholar
[11]Lyndon, R. C., Properties preserved under homomorphism, Pacific journal of mathematics, vol. 9 (1959), pp. 143–154.CrossRefGoogle Scholar
[12]Makkai, M., On PCΔ-classes in the theory of models, A Magyar Tudományos Akademia Matematikai Kutató Intézetének Közleményei, vol. 9 (1964), pp. 159–194.Google Scholar
[13]Makkai, M., (a) Preservation theorems for infinitary logic; (b) Model theoretic results on infinitary sentences, Notices of the American Mathematical Society, vol. 15 (1968), p. 196, 68T-24; p. 639, 68T-464.Google Scholar
[14]Makkai, M., Applications of a method of Smullyan's to logics on admissible sets (to appear).Google Scholar
[15]Malitz, J., Problems in the model theory of infinite languages, Doctoral Dissertation, University of California, Berkeley, Calif., 1965.Google Scholar
[16]Scott, D. S., Logic with denumerably long formulas and finite strings of quantifiers. The theory of models. Proceedings of the 1963 International Symposium at Berkeley, North-Holland, Amsterdam, 1965, pp. 329–341.Google Scholar
[17]Smullyan, R. M., A unifying principal in quantification theory, Proceedings of the National Academy of Science U.S.A., vol. 49 (1963), pp. 828–832.CrossRefGoogle ScholarPubMed
[18]Smullyan, R. M., A unifying principle in quantification theory. The theory of models, Proceedings of the 1963 International Symposium at Berkeley, North-Holland, Amsterdam, 1965, pp. 433–434.Google Scholar
[19]Tarski, A., Contributions to the theory of models. I, II, Koninklijke Nederlandse Academie van Wetenschappen. Proceedings. Series A, vol. 57 (1954), pp. 572–581, 582-588 = Indagationes mathematicae, vol. 16 (1954), pp. 572-581, 582-588.Google Scholar