MATH 6830

MATH 6830

Course information provided by the Courses of Study 2017-2018.

Introduction to model theory at the level of the books by Hodges or Chang and Keisler.

When Offered Spring (offered alternate years).

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Syllabi: none
  •   Regular Academic Session. 

  • 4 Credits Stdnt Opt

  • 16001 MATH 6830   LEC 001

  • This course will given an introduction to model theory, taught from a more algebraic perspective. We will start by reviewing the compactness and completeness theorem. The goal of the course is to prove Morley's Categoricity Theorem, which characterizes when the isomorphism type of an uncountable model of a given theory is determined by its cardinality. Along the way, we will develop several concepts and tools which are important in their own right: the Lowenheim-Skolem theorem, the Vaught's test for the completeness of a first order theory, quantifier elimination, back and forth arguments, quantifier elimination, stability, and indiscernability. Students should ideally have had some exposure to predicate logic (structures, satisfaction, proof, the completeness theorem), although a properly motivated student can pick up the relevant knowledge as it is reviewed.