Abstract
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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