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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| Published in: | Siberian mathematical journal Vol. 59; no. 6; pp. 1014 - 1023 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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Moscow
Pleiades Publishing
01.11.2018
Springer Nature B.V |
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| ISSN: | 0037-4466, 1573-9260 |
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| 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 Δ-definable in the basic language. |
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| AbstractList | 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. |
| Author | Sviridenko, D. I. Goncharov, S. S. |
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| Cites_doi | 10.1134/S0037446617050068 10.1007/3-540-16444-8_13 10.1007/3-540-18740-5_28 10.1142/9781848162778_0006 10.1023/B:ALLO.0000028930.44605.68 |
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| Keywords | 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 |
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| References | Ershov, Goncharov, Sviridenko (CR5) 1986; 31 Ershov (CR10) 1996 Goncharov (CR11) 1986; 114 Goncharov (CR1) 2017; 58 Goncharov, Sviridenko (CR6) 1986; 31 Ershov (CR9) 1983; 28 Ospichev, Ponomarev (CR16) 2018; 15 Goncharov, Sviridenko (CR3) 1987; 120 Goncharov, Sviridenko (CR4) 1986; 215 Ershov, Goncharov, Sviridenko (CR7) 1987; 278 Ershov (CR8) 1983; 27 Ershov, Puzarenko, Stukachev (CR14) 2011 Goncharov, Sviridenko (CR2) 1989; 142 Goncharov (CR12) 1989; 143 Ershov, Goncharov, Nerode, Remmel (CR13) 1998 Morozov, Puzarenko (CR15) 2004; 43 S. S. Goncharov (445_CR4) 1986; 215 Yu. L. Ershov (445_CR13) 1998 Yu. L. Ershov (445_CR9) 1983; 28 Yu. L. Ershov (445_CR8) 1983; 27 S. S. Goncharov (445_CR12) 1989; 143 S. S. Goncharov (445_CR6) 1986; 31 S. Ospichev (445_CR16) 2018; 15 Yu. L. Ershov (445_CR14) 2011 A. S. Morozov (445_CR15) 2004; 43 S. S. Goncharov (445_CR11) 1986; 114 S. S. Goncharov (445_CR3) 1987; 120 Yu. L. Ershov (445_CR7) 1987; 278 S. S. Goncharov (445_CR1) 2017; 58 S. S. Goncharov (445_CR2) 1989; 142 Yu. L. Ershov (445_CR5) 1986; 31 Yu. L. Ershov (445_CR10) 1996 |
| References_xml | – volume: 142 start-page: 101 year: 1989 end-page: 121 ident: CR2 article-title: Σ-Programming publication-title: Trans. Amer. Math. Soc. – volume: 58 start-page: 794 issue: 5 year: 2017 end-page: 800 ident: CR1 article-title: Conditional terms in semantic programming publication-title: Sib. Math. J. doi: 10.1134/S0037446617050068 – volume: 27 start-page: 670 issue: 4 year: 1983 end-page: 672 ident: CR8 article-title: The principle of Σ-enumeration publication-title: Soviet Math. Dokl. – volume: 15 start-page: 987 year: 2018 end-page: 995 ident: CR16 article-title: A note on the complexity of formulas in semantic programming publication-title: Sib. Elektron. Mat. Izv. – volume: 215 start-page: 169 year: 1986 end-page: 179 ident: CR4 article-title: Theoretical aspects of Σ-programming publication-title: Lect. Notes Comput. Sci. doi: 10.1007/3-540-16444-8_13 – volume: 143 start-page: 139 year: 1989 end-page: 152 ident: CR12 article-title: Data models and languages for their description publication-title: Trans. Amer. Math. Soc. – volume: 31 start-page: 608 issue: 6 year: 1986 end-page: 610 ident: CR6 article-title: Mathematical bases of semantic programming publication-title: Soviet Math. Dokl. – year: 1996 ident: CR10 publication-title: Definability and Computability – volume: 278 start-page: 116 year: 1987 end-page: 122 ident: CR7 article-title: Semantic foundations of programming publication-title: Lect. Notes Comput. Sci. doi: 10.1007/3-540-18740-5_28 – volume: 120 start-page: 24 year: 1987 end-page: 51 ident: CR3 article-title: Σ-Programming and their semantics publication-title: Vychisl. Systemy – start-page: 169 year: 2011 end-page: 242 ident: CR14 article-title: HF-computability publication-title: Computability in Context, Imperial College Press doi: 10.1142/9781848162778_0006 – volume: 28 start-page: 739 issue: 5 year: 1983 end-page: 742 ident: CR9 article-title: Dynamic logic over admissible sets publication-title: Soviet Math. Dokl. – volume: 31 start-page: 1113 year: 1986 end-page: 1120 ident: CR5 article-title: Semantic programming publication-title: Information Processing 86. Proc. IFIP 10th World Comput. Congress, Dublin – volume: 43 start-page: 162 issue: 3 year: 2004 end-page: 178 ident: CR15 article-title: Σ-subsets of natural numbers publication-title: Algebra and Logic doi: 10.1023/B:ALLO.0000028930.44605.68 – volume: 114 start-page: 84 year: 1986 end-page: 95 ident: CR11 article-title: The theory of lists, and its models publication-title: Vychisl. Systemy – year: 1998 ident: CR13 publication-title: Introduction to the Handbook of Recursive Mathematics – volume: 120 start-page: 24 year: 1987 ident: 445_CR3 publication-title: Vychisl. Systemy – volume: 28 start-page: 739 issue: 5 year: 1983 ident: 445_CR9 publication-title: Soviet Math. Dokl. – volume: 58 start-page: 794 issue: 5 year: 2017 ident: 445_CR1 publication-title: Sib. Math. J. doi: 10.1134/S0037446617050068 – volume: 278 start-page: 116 year: 1987 ident: 445_CR7 publication-title: Lect. Notes Comput. Sci. doi: 10.1007/3-540-18740-5_28 – volume: 15 start-page: 987 year: 2018 ident: 445_CR16 publication-title: Sib. Elektron. Mat. Izv. – volume: 27 start-page: 670 issue: 4 year: 1983 ident: 445_CR8 publication-title: Soviet Math. Dokl. – volume: 43 start-page: 162 issue: 3 year: 2004 ident: 445_CR15 publication-title: Algebra and Logic doi: 10.1023/B:ALLO.0000028930.44605.68 – volume-title: Introduction to the Handbook of Recursive Mathematics year: 1998 ident: 445_CR13 – volume: 215 start-page: 169 year: 1986 ident: 445_CR4 publication-title: Lect. Notes Comput. Sci. doi: 10.1007/3-540-16444-8_13 – volume-title: Definability and Computability year: 1996 ident: 445_CR10 – start-page: 169 volume-title: Computability in Context, Imperial College Press year: 2011 ident: 445_CR14 doi: 10.1142/9781848162778_0006 – volume: 142 start-page: 101 year: 1989 ident: 445_CR2 publication-title: Trans. Amer. Math. Soc. – volume: 114 start-page: 84 year: 1986 ident: 445_CR11 publication-title: Vychisl. Systemy – volume: 143 start-page: 139 year: 1989 ident: 445_CR12 publication-title: Trans. Amer. Math. Soc. – volume: 31 start-page: 608 issue: 6 year: 1986 ident: 445_CR6 publication-title: Soviet Math. Dokl. – volume: 31 start-page: 1113 year: 1986 ident: 445_CR5 publication-title: Information Processing 86. Proc. IFIP 10th World Comput. Congress, Dublin |
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| Title | Recursive Terms in Semantic Programming |
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