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Algebra Logika, 2003, Volume 42, Number 4, Pages 391–412 (Mi al37)  

Constructive and Non-Constructive Infinite Formulas in Computable Structures

P. E. Alaev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: A transition from arbitrary $L_{\omega_1\omega}$-formulas to computable formulas in the class of computable structures is considered. It is shown that transition of a certain type is possible which doubles the complexity of the formulas. In addition, the complexity jump is analyzed for the transition from an arbitrary Scott family consisting of $L_{\omega_1\omega}$-formulas to a computable Scott family in a fixed computable structure. Exact estimates of this jump are found.

Keywords: computable structure, computable formula, Scott family.

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English version:
Algebra and Logic, 2003, 42:4, 219–231

Bibliographic databases:

UDC: 510.5+510.67
Received: 27.04.2001
Revised: 01.08.2002

Citation: P. E. Alaev, “Constructive and Non-Constructive Infinite Formulas in Computable Structures”, Algebra Logika, 42:4 (2003), 391–412; Algebra and Logic, 42:4 (2003), 219–231

Citation in format AMSBIB
\Bibitem{Ala03}
\by P.~E.~Alaev
\paper Constructive and Non-Constructive Infinite Formulas in Computable Structures
\jour Algebra Logika
\yr 2003
\vol 42
\issue 4
\pages 391--412
\mathnet{http://mi.mathnet.ru/al37}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2017511}
\zmath{https://zbmath.org/?q=an:1034.03047}
\transl
\jour Algebra and Logic
\yr 2003
\vol 42
\issue 4
\pages 219--231
\crossref{https://doi.org/10.1023/A:1025053225562}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42349106964}


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