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

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Abstract: A monotone formula in the infinitary logic 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 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 .

**[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.

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DOI:
https://doi.org/10.1090/S0002-9939-1977-0441686-2

Article copyright:
© Copyright 1977
American Mathematical Society