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An $L_{\omega _{1}\omega }$ complete and consistent theory without models

Authors: M. Makkai and J. Mycielski
Journal: Proc. Amer. Math. Soc. 62 (1977), 131-133
MSC: Primary 02B25
MathSciNet review: 0439578
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Abstract: We simplify the example of Ryll-Nardzewski of an ${L_{{\omega _1}\;\omega }}$ theory with the above properties. We include other facts on the relationship of logic to 01-laws and on the ${L_{{\omega _1}\;\omega }}$ definability of some sets which are meager but of full measure.

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  • Dana Scott, Logic with denumerably long formulas and finite strings of quantifiers, Theory of Models (Proc. 1963 Internat. Sympos. Berkeley), North-Holland, Amsterdam, 1965, pp. 329–341. MR 0200133
  • H. Jerome Keisler, Model theory for infinitary logic. Logic with countable conjunctions and finite quantifiers, North-Holland Publishing Co., Amsterdam-London, 1971. Studies in Logic and the Foundations of Mathematics, Vol. 62. MR 0344115
  • J. Mycielski, Measure and category of some sets of models, Notices Amer. Math. Soc. 22 (1975), A-475-A-476. Abstract 75T-E43.

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Article copyright: © Copyright 1977 American Mathematical Society