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A theory of formal truth arithmetically equivalent to \(ID_ 1\). (English) Zbl 0713.03029

The author presents a theory VF of partial truth over Peano arithmetic and proves that this theory has the same arithmetical theorems as the theory of elementary inductive definitions \((ID_ 1)\). The language \(L_{VF}\) of VF consists of the language of Peano arithmetic and a unary predicate symbol T. The notion of term is recursively defined using arithmetical functions (successor, addition and multiplication), and formulas are defined, using as atoms the predicate of equality and the predicate T. Other function-symbols are used for defining primitive recursion. Syntactical and semantical properties of \(L_{VF}\) become provable in a fragment of Peano arithmetic, owing to a standard Gödel numbering.
Reviewer: N.Both

MSC:

03F30 First-order arithmetic and fragments
03F40 Gödel numberings and issues of incompleteness
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References:

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