We study a generalized interpretation method for proving the decidability of theories. This method is used to prove the decidability of the theory of the lattice of continuous functions from ℝ to ℝ. We prove that the theory of the structure of continuous functions extended by one unary predicate becomes undecidable.
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Translated from Vestnik Novosibirskogo Gosudarstvennogo Universiteta: Seriya Matematika, Mekhanika, Informatika 12, No. 3, 2012, pp. 22–34.
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Amstislavskiy, V.S. Elementary Theories of Spaces of Continuous Functions. J Math Sci 202, 13–24 (2014). https://doi.org/10.1007/s10958-014-2030-9
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DOI: https://doi.org/10.1007/s10958-014-2030-9