Geodesic
On the lattices of continuous functions
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 15 (2015) no. 1, pp. 3-20

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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. 
V. S. Amstislavskiy. On the lattices of continuous functions. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 15 (2015) no. 1, pp. 3-20. http://geodesic.mathdoc.fr/item/VNGU_2015_15_1_a0/
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