Results 41 to 50 of about 86 (68)
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Consistency of Heyting arithmetic in natural deduction
Mathematical Logic Quarterly, 2010AbstractA proof of the consistency of Heyting arithmetic formulated in natural deduction is given. The proof is a reduction procedure for derivations of falsity and a vector assignment, such that each reduction reduces the vector. By an interpretation of the expressions of the vectors as ordinals each derivation of falsity is assigned an ordinal less ...
Annika Kanckos
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On the structure of kripke models of heyting arithmetic
Mathematical Logic Quarterly, 1993AbstractSince in Heyting Arithmetic (HA) all atomic formulas are decidable, a Kripke model for HA may be regarded classically as a collection of classical structures for the language of arithmetic, partially ordered by the submodel relation. The obvious question is then: are these classical structures models of Peano Arithmetic (PA)?
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From Heyting Arithmetic to Peano Arithmetic
1998Peano Arithmetic (PA) is classical first-order number theory; it differs from Heyting Arithmetic (HA) only in including the Excluded Middle, A V ⌝A. I shall obtain PA from HA by a variation, due to Gentzen (1933), of Godel’s (1933a) double-negation interpretation. It follows that every theorem of PA (without free variables) has, via its HA, LPT and CPF
Fletcher Peter
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Strictly Positive Fragments of the Provability Logic of Heyting Arithmetic
Studia LogicaAbstract We determine the strictly positive fragment $$\textsf{QPL}^+(\textsf{HA})$$ QPL +
Ana De Almeida Borges +2 more
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The creative subject and Heyting's arithmetic [PDF]
Banach Center Publications, 1982 exaly +2 more sources
Second-Order Heyting Arithmetic
1998Second-Order Heyting Arithmetic (2HA) is obtained from Heyting Arithmetic (HA, Chapter 32) as follows. Metavariables that denote variables will be interpreted as follows.
Fletcher Peter
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A formal system of negationless arithmetic that is conservative with respect to heyting arithmetic
Mathematical Notes, 1984A 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.
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Intuitionistic sets and numbers: small set theory and Heyting arithmetic
Archive for Mathematical LogicAbstract It has long been known that (classical) Peano arithmetic is, in some strong sense, “equivalent” to the variant of (classical) Zermelo–Fraenkel set theory (including choice) in which the axiom of infinity is replaced by its negation. The intended model of the latter is the set of hereditarily finite sets.
Stewart Shapiro +2 more
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Fragments of Heyting arithmetic
Journal of Symbolic Logic, 2000AbstractWe define classes Φnof formulae of first-order arithmetic with the following properties:(i) Everyφϵ Φnis classically equivalent to a Πn-formula (n≠ 1, Φ1:= Σ1).(ii)(iii)IΠnandiΦn(i.e., Heyting arithmetic with induction schema restricted to Φn-formulae) prove the same Π2-formulae.We further generalize a result by Visser and Wehmeier. namely that
openaire +1 more source