It is proved that any countable consistent theory with infinite models has a Σ-presentable model of cardinality 2ω over ℍ𝔽(ℝ). It is shown that some structures studied in analysis (in particular, a semigroup of continuous functions, certain structures of nonstandard analysis, and infinite-dimensional separable Hilbert spaces) have no simple Σ-presentations in hereditarily finite superstructures over existentially Steinitz structures. The results are proved by a unified method on the basis of a new general sufficient condition.
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Supported by RFBR, projects No. 14-01-00376 and 13-01-91001-ANF-a.
Translated from Algebra i Logika, Vol. 56, No. 6, pp. 691-711, November-December, 2017.
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Morozov, A.S. Nonpresentability of Some Structures of Analysis in Hereditarily Finite Superstructures. Algebra Logic 56, 458–472 (2018). https://doi.org/10.1007/s10469-018-9468-7
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DOI: https://doi.org/10.1007/s10469-018-9468-7