Quantifier elimination for infinite terms
Identifieur interne : 002C18 ( Istex/Corpus ); précédent : 002C17; suivant : 002C19Quantifier elimination for infinite terms
Auteurs : G. Marongiu ; S. TulipaniSource :
- Archive for Mathematical Logic [ 0933-5846 ] ; 1991-01-01.
English descriptors
- Teeft :
- Algebra, Arity, Atomic formulas, Axiom, Berlin heidelberg, Canonical morphism, Complete extensions, Complete theories, Constant symbols, Domain closure axiom, Domain tree, Elementary equations, Final value, Finite signature, Finite terms, First order formula, First order language, First order theory, First order variables, Free algebras, Freeness axioms, Function symbol, Function symbols, Induction hypothesis, Infinite signature, Infinite terms, Infinite trees, Inverse functions, Inverse symbols, Inverse term, Inverse terms, Logic program, Logic programming, Main result, Marongiu, Maximal pointer, Morphism, Natural number, Next lemma, Ordinary term, Pointer, Positive depth, Predicate symbol, Procedure elem, Quantifier, Quantifier elimination, Quantifier elimination procedure, Rational terms, Rational trees, Same argument, Semantics, Signature, Syntactic terms, Trivial case, Trivial equation, Tulipani, Unique element, Universal closure.
Abstract
Abstract: We consider the theoryT IT of infinite terms. The axioms for the theoryT IT are analogous to the Mal'cev's axioms for the theoryT IT of finite terms whose models are the locally free algebras. Recently Maher [Ma] has proved that the theoryT IT in a finite non singular signature plus the Domain Closure Axiom is complete. We give a description of all the complete extension ofT IT from which an effective decision procedure forT IT is obtained. Our approach considers formulas built up with syntactic terms containing pointers. Using such a technique, the analysis of the theoryT IT can be carried out in analogy with Mal'cev's analysis ofT FT. Our results follow from an effective quantifier elimination procedure for formulas with pointers.
Url:
DOI: 10.1007/BF01370691
Links to Exploration step
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<name type="personal"><namePart type="given">G.</namePart>
<namePart type="family">Marongiu</namePart>
<affiliation>Dipartimento di Matematica, Piazza di Porta San Donato 5, I-40127, Bologna, Italy</affiliation>
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<name type="personal" displayLabel="corresp"><namePart type="given">S.</namePart>
<namePart type="family">Tulipani</namePart>
<affiliation>Dipartimento di Matematica e Fisica, I-62032, Camerino (MC), Italy</affiliation>
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<originInfo><publisher>Springer-Verlag</publisher>
<place><placeTerm type="text">Berlin/Heidelberg</placeTerm>
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<dateCreated encoding="w3cdtf">1989-08-04</dateCreated>
<dateIssued encoding="w3cdtf">1991-01-01</dateIssued>
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<abstract lang="en">Abstract: We consider the theoryT IT of infinite terms. The axioms for the theoryT IT are analogous to the Mal'cev's axioms for the theoryT IT of finite terms whose models are the locally free algebras. Recently Maher [Ma] has proved that the theoryT IT in a finite non singular signature plus the Domain Closure Axiom is complete. We give a description of all the complete extension ofT IT from which an effective decision procedure forT IT is obtained. Our approach considers formulas built up with syntactic terms containing pointers. Using such a technique, the analysis of the theoryT IT can be carried out in analogy with Mal'cev's analysis ofT FT. Our results follow from an effective quantifier elimination procedure for formulas with pointers.</abstract>
<relatedItem type="host"><titleInfo><title>Archive for Mathematical Logic</title>
</titleInfo>
<titleInfo type="abbreviated"><title>Arch Math Logic</title>
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<genre type="journal" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0GLKJH51-B">journal</genre>
<originInfo><publisher>Springer</publisher>
<dateIssued encoding="w3cdtf">1991-01-01</dateIssued>
<copyrightDate encoding="w3cdtf">1991</copyrightDate>
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<subject><genre>Mathematics</genre>
<topic>Mathematics, general</topic>
<topic>Algebra</topic>
<topic>Mathematical Logic and Foundations</topic>
</subject>
<identifier type="ISSN">0933-5846</identifier>
<identifier type="eISSN">1432-0665</identifier>
<identifier type="JournalID">153</identifier>
<identifier type="IssueArticleCount">5</identifier>
<identifier type="VolumeIssueCount">6</identifier>
<part><date>1991</date>
<detail type="volume"><number>31</number>
<caption>vol.</caption>
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<detail type="issue"><number>1</number>
<caption>no.</caption>
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<extent unit="pages"><start>1</start>
<end>17</end>
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<identifier type="DOI">10.1007/BF01370691</identifier>
<identifier type="ArticleID">BF01370691</identifier>
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<accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag, 1991</accessCondition>
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