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Continuous Logic and Probability Algebras
Yang, Fan

2016, Master of Science, Ohio State University, Mathematics.
Continuous logic is a multi-valued logic where the set of truth values is the unit interval
[0, 1]. It was developed recently as a framework for metric structures, which consist of
complete, bounded metric spaces on which there are distinguished elements and
uniformly continuous functions. There are many parallels between continuous logic and
first-order logic: 0 corresponds to true and 1 to false, sup and inf take the place of
quantifiers, and uniformly continuous functions on [0, 1] replace connectives. Instead of
a distinguished equality symbol, there is a distinguished predicate for the metric. Familiar
theorems of first-order logic, such as completeness, compactness, and downward
Lowenheim-Skolem, have modified counterparts in continuous logic. We present these
results in comparison to those in first order logic and prove that the class of probability
algebras (probability spaces modulo null sets where the distance between two events is
their symmetric difference) is axiomatizable in continuous logic.
Christopher Miller (Advisor)
Timothy Carlson (Committee Member)
62 p.

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Yang, F. (2016). Continuous Logic and Probability Algebras . (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Yang, Fan. "Continuous Logic and Probability Algebras ." Electronic Thesis or Dissertation. Ohio State University, 2016. OhioLINK Electronic Theses and Dissertations Center. 23 Nov 2017.

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Yang, Fan "Continuous Logic and Probability Algebras ." Electronic Thesis or Dissertation. Ohio State University, 2016. https://etd.ohiolink.edu/

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