Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya Matematika, Mekhanika, Informatika
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Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya Matematika, Mekhanika, Informatika, 2015, Volume 15, Issue 1, Pages 3–20 (Mi vngu358)  
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
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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.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00015a
Received: 03.06.2014
English version:
Journal of Mathematical Sciences, 2016, Volume 215, Issue 4, Pages 421–435
DOI: https://doi.org/10.1007/s10958-016-2848-4
Document Type: Article
UDC: 510.665, 510.67
Language: Russian
Citation: V. S. Amstislavskiy, “On the lattices of continuous functions”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 15:1 (2015), 3–20; J. Math. Sci., 215:4 (2016), 421–435
Citation in format AMSBIB
\Bibitem{Ams15}
\by V.~S.~Amstislavskiy
\paper On the lattices of continuous functions
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2015
\vol 15
\issue 1
\pages 3--20
\mathnet{http://mi.mathnet.ru/vngu358}
\transl
\jour J. Math. Sci.
\yr 2016
\vol 215
\issue 4
\pages 421--435
\crossref{https://doi.org/10.1007/s10958-016-2848-4}
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    		Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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