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Fan Yang thesis 2.pdf (434.54 KB)
ETD Abstract Container
Abstract Header
Continuous Logic and Probability Algebras
Author Info
Yang, Fan
ORCID® Identifier
http://orcid.org/0000-0003-3576-0977
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1450701248
Abstract Details
Year and Degree
2016, Master of Science, Ohio State University, Mathematics.
Abstract
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.
Committee
Christopher Miller (Advisor)
Timothy Carlson (Committee Member)
Pages
62 p.
Subject Headings
Mathematics
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Citations
Yang, F. (2016).
Continuous Logic and Probability Algebras
[Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1450701248
APA Style (7th edition)
Yang, Fan.
Continuous Logic and Probability Algebras .
2016. Ohio State University, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1450701248.
MLA Style (8th edition)
Yang, Fan. "Continuous Logic and Probability Algebras ." Master's thesis, Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1450701248
Chicago Manual of Style (17th edition)
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Document number:
osu1450701248
Download Count:
604
Copyright Info
© 2016, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.