A Sufficient Condition for Nonpresentability of Structures in Hereditarily Finite Superstructures

We introduce a class of existentially Steinitz structures containing, in particular, the fields of real and complex numbers. A general result is proved which implies that if M is an existentially Steinitz structure then the following structures cannot be embedded in any structure Σ-presentable with...

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Bibliographic Details
Published in:Algebra and logic 2016-07, Vol.55 (3), p.242-251
Main Author: Morozov, A. S.
Format: Article
Language:English
Subjects:
Algebra
Algebraic structures
Boolean algebra
Complex numbers
Embedded structures
Group theory
Mathematical Logic and Foundations
Mathematical research
Mathematics
Mathematics and Statistics
Permutations
Real numbers
Set theory
Superstructures
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Summary:We introduce a class of existentially Steinitz structures containing, in particular, the fields of real and complex numbers. A general result is proved which implies that if M is an existentially Steinitz structure then the following structures cannot be embedded in any structure Σ-presentable with trivial equivalence over ℍ F ( M ): the Boolean algebra of all subsets of ω , its factor modulo the ideal consisting of finite sets, the group of all permutations on ω , its factor modulo the subgroup of all finitary permutations, the semigroup of all mappings from ω to ω , the lattice of all open sets of real numbers, the lattice of all closed sets of real numbers, the group of all permutations of ℝ Σ-definable with parameters over ℍ F (ℝ), and the semigroup of such mappings from ℝ to ℝ.
ISSN:0002-5232
1573-8302
DOI:10.1007/s10469-016-9392-7