On the lattices of continuous functions

V. S. Amstislavskiy

A.P. Ershov Institute of Informatics Systems, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: We study some new applications of the generalized method of interpretations to prove decidability of the theories of some popular structures in analysis. Earlier we proved decidability of the theory of a real continuous functions lattice by this method. In this work we generalize the lattice of real continuous functions to an algebraic structure of continuous functions over a perfectly normal space. By the generalized method of interpretations we prove decidability of the theory of this structure under some conditions.

Keywords: elementary theory, lattice of continuous functions, decidability of theories, perfectly normal space, generalized method of interpretations.

UDC: 510.665, 510.67

Received: 03.06.2014

 English version: Journal of Mathematical Sciences, 2016, 215:4, 421–435