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Remarks on abstract Galois theory

2011; UNIVERSIDADE ESTADUAL DE CAMPINAS; Volume: 34; Issue: 1 Linguagem: Inglês

10.1590/s0100-60452011000100008

2317-630X

Newton C. A. da Costa, Otávio Bueno,

Advanced Topology and Set Theory

This paper is a historical companion to a previous one, in which it was studied the so-called abstract Galois theory as formulated by the Portuguese mathematician José Sebastião e Silva (see da Costa, Rodrigues (2007)). Our purpose is to present some applications of abstract Galois theory to higher-order model theory, to discuss Silva's notion of expressibility and to outline a classical Galois theory that can be obtained inside the two versions of the abstract theory, those of Mark Krasner and of Silva. Some comments are made on the universal theory of (set-theoretic) structures.