A formal system of negationless arithmetic that is conservative with respect to heyting arithmetic
Copyright policy )A formal system of negationless arithmetic that is conservative with respect to heyting arithmetic
A system of natural deduction for a negationless arithmetic is presented. A deduction in \(HA^ N\) is defined as a pair of deductions \(\), where \(\Sigma_ 1\) is a proof of nonemptiness of the conjunction of all open hypotheses of \(\Sigma_ 2\) and \(\Sigma_ 2\) is a deduction in a classical sense. Natural interpretations of HA in \(HA^ N\) and \(HA^ N\) in HA are introduced. Appropriate interpretation results are proven showing in particular that HA is a conservative extension of \(HA^ N\) with respect to the interpretation.
- Lomonosov Moscow State University Russian Federation
First-order arithmetic and fragments, Structure of proofs, natural deduction, Intuitionistic mathematics, interpretation
First-order arithmetic and fragments, Structure of proofs, natural deduction, Intuitionistic mathematics, interpretation
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