Abstract: We investigate combinations of structures by families of structures relative to families of unary predicates and equivalence relations. Conditions preserving !-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 !-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 Ei-classes do not approximate infinitely many n-ypes for n 2^omega. The theory of disjoint P-combination is Ehrenfeucht if and only if the set ofindexes 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.

Cite: Sudoplatov S.V.
Combinations of structures
Известия Иркутского государственного университета. Серия: Математика (Bulletin of Irkutsk State University. Series Mathematics). 2018. V.24. P.82-101. DOI: 10.26516/1997-7670.2018.24.82 WOS РИНЦ OpenAlex

Dates:

Submitted:	Apr 19, 2018
Published print:	Jun 26, 2018
Published online:	Jun 26, 2018

Identifiers:

Web of science:	WOS:000476651200007
Elibrary:	35125012
OpenAlex:	W2964309876

Citing:

DB	Citing
Web of science	14
Elibrary	26
OpenAlex	15

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