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C. C. Chang | |
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| Born | 1927 Tianjin, China |
| Died | July 17, 2014 (aged 86 or 87) Santa Clarita, California |
| Known for | Chang's conjecture |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of California, Los Angeles |
| Doctoral advisor | Alfred Tarski |
Chen Chung Chang (Chinese :张晨钟) was a mathematician who worked in model theory. He obtained his PhD from Berkeley in 1955 on "Cardinal and Ordinal Factorization of Relation Types" under Alfred Tarski. He wrote the standard text Chang & Keisler (1990) on model theory. Chang's conjecture and Chang's model are named after him. He also proved the ordinal partition theorem (expressed in the arrow notation for Ramsey theory) ωω→(ωω,3)2, originally a problem of Erdős and Hajnal. He also introduced MV-algebras as models for Łukasiewicz logic. Chang was a professor at the mathematics department of the University of California, Los Angeles.
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In mathematical logic, model theory is the study of the relationship between formal theories, and their models. The aspects investigated include the number and size of models of a theory, the relationship of different models to each other, and their interaction with the formal language itself. In particular, model theorists also investigate the sets that can be defined in a model of a theory, and the relationship of such definable sets to each other. As a separate discipline, model theory goes back to Alfred Tarski, who first used the term "Theory of Models" in publication in 1954. Since the 1970s, the subject has been shaped decisively by Saharon Shelah's stability theory.
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In model theory, a branch of mathematical logic, two structures M and N of the same signature σ are called elementarily equivalent if they satisfy the same first-order σ-sentences.
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In model theory, a branch of mathematical logic, the spectrum of a theory is given by the number of isomorphism classes of models in various cardinalities. More precisely, for any complete theory T in a language we write I(T, κ) for the number of models of T (up to isomorphism) of cardinality κ. The spectrum problem is to describe the possible behaviors of I(T, κ) as a function of κ. It has been almost completely solved for the case of a countable theory T.
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Howard Jerome Keisler is an American mathematician, currently professor emeritus at University of Wisconsin–Madison. His research has included model theory and non-standard analysis.
In model theory, a branch of mathematical logic, the notion of an existentially closed model of a theory generalizes the notions of algebraically closed fields, real closed fields, existentially closed groups, and dense linear orders without endpoints.
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In model theory, a branch of mathematical logic, Chang's conjecture, attributed to Chen Chung Chang by Vaught, states that every model of type (ω2,ω1) for a countable language has an elementary submodel of type. A model is of type (α,β) if it is of cardinality α and a unary relation is represented by a subset of cardinality β. The usual notation is .
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