Recursive Terms in Semantic Programming
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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.
Keywordsformula term restricted quantifier Δ0-formula Δ-formula Σ-formula semantic programming computability computability over abstract structures conditional term recursive term model hereditary finite list hereditary finite set
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