Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The monotone class theorem in infinitary logic


Author: H. Jerome Keisler
Journal: Proc. Amer. Math. Soc. 64 (1977), 129-134
MSC: Primary 02B25
DOI: https://doi.org/10.1090/S0002-9939-1977-0441686-2
MathSciNet review: 0441686
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A monotone formula in the infinitary logic $ {L_{{\omega _1}\omega }}$ is a formula which is built up from finite formulas using only quantifiers and monotone countable conjunctions and disjunctions. The monotone class theorem from measure theory is used to show that every formula of $ {L_{{\omega _1}\omega }}$ is logically equivalent to a monotone formula (the monotone normal form theorem). The proof is effectivized in order to obtain similar normal form theorems for admissible logics $ {L_A}$.


References [Enhancements On Off] (What's this?)

  • [1] Jon Barwise, Admissible sets and structures, Springer-Verlag, Berlin-New York, 1975. An approach to definability theory; Perspectives in Mathematical Logic. MR 0424560
  • [2] Paul R. Halmos, Measure Theory, D. Van Nostrand Company, Inc., New York, N. Y., 1950. MR 0033869
  • [3] Model theory, Handbook of mathematical logic, Part A, North-Holland, Amsterdam, 1977, pp. 3–313. Studies in Logic and the Foundations of Math., Vol. 90. With contributions by Jon Barwise, H. Jerome Keisler, Paul C. Eklof, Angus Macintyre, Michael Morley, K. D. Stroyan, M. Makkai, A. Kock and G. E. Reyes. MR 0491125
  • [4] S. Saks, Theory of the integral, Warsaw, 1937.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 02B25

Retrieve articles in all journals with MSC: 02B25


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0441686-2
Article copyright: © Copyright 1977 American Mathematical Society