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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
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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] J. Barwise, Admissible sets and structures, Springer-Verlag, Berlin and New York, 1975. MR 0424560 (54:12519)
  • [2] P. Halmos, Measure theory, Van Nostrand, Princeton, N. J., 1950. MR 11, 504. MR 0033869 (11:504d)
  • [3] H. J. Keisler, Hyperfinite model theory, (Proc. 1976 Oxford Logic Sympos.), (to appear). MR 0491125 (58:10395)
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DOI: https://doi.org/10.1090/S0002-9939-1977-0441686-2
Article copyright: © Copyright 1977 American Mathematical Society

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