Nonpresentability of Some Structures of Analysis in Hereditarily Finite Superstructures

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It is proved that any countable consistent theory with infinite models has a Σ-presentable model of cardinality 2ω over. 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.

Original languageEnglish
Pages (from-to)458-472
Number of pages15
JournalAlgebra and Logic
Issue number6
Publication statusPublished - 1 Jan 2018


  • countable consistent theory
  • existentially Steinitz structure
  • hereditarily finite superstructure
  • infinitedimensional separable Hilbert space
  • nonstandard analysis
  • semigroup of continuous functions
  • Σ-presentability
  • Sigma-presentability
  • infinite-dimensional separable Hilbert space


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