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Teoria modeli i dynamika topologiczna

Newelski L.

Roczniki Polskiego Towarzystwa Matematycznego. Seria 2: Wiadomości Matematyczne

2008

[Z] 44

1-13

In the first part the article contains an exposition of introductory notions of model theory. The second part is devoted to a new research direction in model theory, related to topological dynamics. Several connections between the notions of model theory and topological dynamics are discussed. In particular, a model-theoretic perspective on the Ellis semigroup is skeched.

A model-theoretic criterion for quantifier elimination and its application to geometry

Nowak K.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 4

377-381

In this paper we present a model-theoretic criterion for quantifier elimination being a variant of Shoenfield's theorem (see [1], Chap. V, [paragraph]5). Our short proof is based directly on Godel's completeness and compactness theorems as well as on the concept of diagrams, and does not involve model-completeness or Robinson's test as does for instance the proof of certain related criteria given in [2], Chap. VIII, [paragraph]4. As a consequence, we immediately obtain the theorems of Chevalley and Tarski-Seidenberg from algebraic and semialalgebraic geometry.