An 𝐿_{𝜔₁𝜔} complete and consistent theory without models

Makkai, M.; Mycielski, J.

doi:10.1090/S0002-9939-1977-0439578-8

An $L\sb{\omega \sb{1}\omega }$ complete and consistent theory without models

Authors: M. Makkai and J. Mycielski
Journal: Proc. Amer. Math. Soc. 62 (1977), 131-133
MSC: Primary 02B25
DOI: https://doi.org/10.1090/S0002-9939-1977-0439578-8
MathSciNet review: 0439578
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

[1] 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
[2] 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
[3] J. Mycielski, Measure and category of some sets of models, Notices Amer. Math. Soc. 22 (1975), A-475-A-476. Abstract 75T-E43.