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This article is cited in 2 scientific papers (total in 2 papers)
Combinations of structures
S. V. Sudoplatovabc a Sobolev Institute of Mathematics, Novosibirsk, Russian Federation
b Novosibirsk State Technical University, Novosibirsk, Russian Federation
c Novosibirsk
State University, Novosibirsk, Russian Federation
Abstract:
We investigate combinations of structures by families of
structures relative to families of unary predicates and
equivalence relations. Conditions preserving $\omega$-categoricity
and Ehrenfeuchtness under these combinations are characterized.
The notions of $e$-spectra are introduced and possibilities for
$e$-spectra are described.
It is shown that $\omega$-categoricity for disjoint
$P$-combinations means that there are finitely many indexes for
new unary predicates and each structure in new unary predicate is
either finite or $\omega$-categorical. Similarly, the theory of
$E$-combination is $\omega$-categorical if and only if each given
structure is either finite or $\omega$-categorical and the set of
indexes is either finite, or it is infinite and $E_i$-classes do
not approximate infinitely many $n$-types for $n\in\omega$. The
theory of disjoint $P$-combination is Ehrenfeucht if and only if
the set of indexes is finite, each given structure is either
finite, or $\omega$-categorical, or Ehrenfeucht, and some given
structure is Ehrenfeucht.
Variations of structures related to combinations and
$E$-representability are considered.
We introduce $e$-spectra for $P$-combinations and
$E$-combinations, and show that these $e$-spectra can have
arbitrary cardinalities.
The property of Ehrenfeuchtness for $E$-combinations is
characterized in terms of $e$-spectra.
Keywords:
combination of structures, $P$-combination,
$E$-combination, $e$-spectrum.
Received: 19.04.2018
Citation:
S. V. Sudoplatov, “Combinations of structures”, Bulletin of Irkutsk State University. Series Mathematics, 24 (2018), 82–101
Linking options:
https://www.mathnet.ru/eng/iigum340 https://www.mathnet.ru/eng/iigum/v24/p82
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Abstract page: | 150 | Full-text PDF : | 48 | References: | 22 |
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