Ultraproducts, the Compactness Theorem and Applications
نویسنده
چکیده
This is a set of lecture notes used in a course on model theory at Virginia Commonwealth University (Math 591 Topics: Logic and Mathematical Structures), which I taught jointly with Sean Cox in the spring of 2014. Most of the material contained in these notes can be found in the following sources. References: • Chang and Keisler. Model Theory, Studies in Logic and the Foundations of Mathematics, Volume 73, Third Ed., 1990, North Holland. • Endertion. A Mathematical Introduction to Logic, Second Ed., 2001, Harcourt Academic Press. • Rothmaler. Introduction to Model Theory Algebra, Logic and Applications Series, Volume 15, First Ed., 2000, Gordon and Breach.
منابع مشابه
Compactness Theorem for Some Generalized Second-Order Language
For the first-order language the compactness theorem was proved by K. Gödel and A. I. Mal’cev in 1936. In 1955, it was proved by J. Łoś (1955) by means of the method of ultraproducts. Unfortunately, for the usual second-order language the compactness theorem does not hold. Moreover, the method of ultraproducts is also inapplicable to second-order models. A possible way out of this situation is ...
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