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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The monotone class theorem in infinitary logic
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by H. Jerome Keisler PDF
Proc. Amer. Math. Soc. 64 (1977), 129-134 Request permission


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 ${L_A}$.
  • Jon Barwise, Admissible sets and structures, Perspectives in Mathematical Logic, Springer-Verlag, Berlin-New York, 1975. An approach to definability theory. MR 0424560
  • Paul R. Halmos, Measure Theory, D. Van Nostrand Co., Inc., New York, N. Y., 1950. MR 0033869
  • Model theory, Handbook of mathematical logic, Part A, Studies in Logic and the Foundations of Math., Vol. 90, North-Holland, Amsterdam, 1977, pp. 3–313. 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
  • S. Saks, Theory of the integral, Warsaw, 1937.
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 64 (1977), 129-134
  • MSC: Primary 02B25
  • DOI:
  • MathSciNet review: 0441686