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Sibirsk. Mat. Zh., 2018, Volume 59, Number 6, Pages 1279–1290 (Mi smj3043)  

This article is cited in 1 scientific paper (total in 1 paper)

Recursive terms in semantic programming

S. S. Goncharov, D. I. Sviridenko

Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: For constructing an enrichment of a language with restricted quantifiers, we extend the notion of term by the construction of the terms conditional and recursive with respect to lists. We show that the so-obtained extension of the language of formulas with restricted quantifiers over structures with hereditary finite lists is a conservative enrichment and the new terms are $\Delta$-definable in the basic language.

Keywords: formula, term, restricted quantifier, $\Delta_0$-formula, $\Delta$-formula, $\Sigma$-formula, semantic programming, computability, computability over abstract structures, conditional term, recursive term, model, hereditary finite list, hereditary finite set.

Funding Agency Grant Number
Russian Science Foundation 17-11-01176
The authors were supported by the Russian Science Foundation (Grant 17-11-01176).


DOI: https://doi.org/10.17377/smzh.2018.59.605

Full text: PDF file (315 kB)
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English version:
Siberian Mathematical Journal, 2018, 59:6, 1014–1023

Bibliographic databases:

UDC: 510.2+510.3+510.6+51.8+004.8
Received: 17.03.2018

Citation: S. S. Goncharov, D. I. Sviridenko, “Recursive terms in semantic programming”, Sibirsk. Mat. Zh., 59:6 (2018), 1279–1290; Siberian Math. J., 59:6 (2018), 1014–1023

Citation in format AMSBIB
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\paper Recursive terms in semantic programming
\jour Sibirsk. Mat. Zh.
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\vol 59
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\pages 1279--1290
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\crossref{https://doi.org/10.17377/smzh.2018.59.605}
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\vol 59
\issue 6
\pages 1014--1023
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. A. Aleksandrova, N. A. Bazhenov, “O razreshimosti spisochnykh struktur”, Sib. matem. zhurn., 60:3 (2019), 489–505  mathnet  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
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