Teories de primer ordre i els problemes de Tarski

Authors

  • Montserrat Casals Ruiz

Abstract

At the beginning of the 20th century, mathematics suffered a foundational crisis, known as the Grundlagenkrise der Mathematik. To answer the need of formalization of mathematics, mathematical logic underwent a profound development. An important outcome of this development was the birth of a new branch of mathematics - Model Theory, which studies algebraic structures from the viewpoint of mathematical logic. In this article we present this approach, its power and its limitations. We begin by reviewing some classical results, such as theorems of A. Tarski on the fields of complex and real numbers. We then present several grouptheoretic results, including results of W. Szmielew on the first-order theory of abelian groups. We finish with a survey of the recent solution of the Tarski problems on the elementary theory of the free group. This article is based on the talk presented by the author to the XIII Meeting of the Catalan Mathematical Society.

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Published

2013-07-12

How to Cite

Casals Ruiz, M. (2013). Teories de primer ordre i els problemes de Tarski. Butlletí De La Societat Catalana De Matemàtiques, 28(1), 5–49. Retrieved from https://revistes.iec.cat/index.php/BSCM/article/view/81819.001

Issue

Vol. 28 No. 1 (2013)

Section

Articles

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