Recursive Terms in Semantic Programming

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...

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Bibliographic Details
Published in:Siberian mathematical journal Vol. 59; no. 6; pp. 1014 - 1023
Main Authors: Goncharov, S. S., Sviridenko, D. I.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.11.2018
Springer Nature B.V
Subjects:
Mathematics
Mathematics and Statistics
semantic programming
hereditary finite set
computability
computability over abstract structures
restricted quantifier
Σ-formula
Δ
conditional term
recursive term
formula
term
model
Δ-formula
hereditary finite list
ISSN:0037-4466, 1573-9260
Online Access:Get full text
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Summary: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 Δ-definable in the basic language.
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ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446618060058