TY - JOUR

T1 - Nonpresentability of Some Structures of Analysis in Hereditarily Finite Superstructures

AU - Morozov, A. S.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - countable consistent theory

KW - existentially Steinitz structure

KW - hereditarily finite superstructure

KW - infinitedimensional separable Hilbert space

KW - nonstandard analysis

KW - semigroup of continuous functions

KW - Σ-presentability

KW - Sigma-presentability

KW - MODELS

KW - infinite-dimensional separable Hilbert space

UR - http://www.scopus.com/inward/record.url?scp=85042438199&partnerID=8YFLogxK

U2 - 10.1007/s10469-018-9468-7

DO - 10.1007/s10469-018-9468-7

M3 - Article

AN - SCOPUS:85042438199

VL - 56

SP - 458

EP - 472

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 6

ER -