The monotone class theorem in infinitary logic
Author: H. Jerome Keisler
Journal: Proc. Amer. Math. Soc. 64 (1977), 129-134
MSC: Primary 02B25
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 .
-  Jon Barwise, Admissible sets and structures, Springer-Verlag, Berlin-New York, 1975. An approach to definability theory; Perspectives in Mathematical Logic. MR 0424560
-  Paul R. Halmos, Measure Theory, D. Van Nostrand Company, Inc., New York, N. Y., 1950. MR 0033869
-  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
-  S. Saks, Theory of the integral, Warsaw, 1937.
- J. Barwise, Admissible sets and structures, Springer-Verlag, Berlin and New York, 1975. MR 0424560 (54:12519)
- P. Halmos, Measure theory, Van Nostrand, Princeton, N. J., 1950. MR 11, 504. MR 0033869 (11:504d)
- H. J. Keisler, Hyperfinite model theory, (Proc. 1976 Oxford Logic Sympos.), (to appear). MR 0491125 (58:10395)
- S. Saks, Theory of the integral, Warsaw, 1937.
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