Name: The intuitionistic propositional calculus with quantifiers
Creator: S. K. Sobolev
Keywords: Categoricity and completeness of theories, Decidability of theories and sets of sentences, Logic with extra quantifiers and operators, intuitionistic propositional calculus with quantifiers, 0102 computer and information sciences, 0101 mathematics, Other nonclassical logic, Intuitionistic mathematics, 01 natural sciences, completeness theorem

descriptionPublicationkeyboard_double_arrow_right Article 01 Jul 1977 English Publisher:Springer Science and Business Media LLCJournal:Mathematical Notes of the Academy of Sciences of the USSR, volume 22, pages 528-532 (issn: 0001-4346, eissn: 1573-8876,

Authors: S. K. Sobolev;

doi: 10.1007/bf01147694

The intuitionistic propositional calculus with quantifiers

- Summary
- Subjects
- Metrics

Abstract

Let L be the language of the intuitionistic propositional calculus J completed by the quantifiers ∀ and ∃, and let calculus 2J in language L contain, besides the axioms of J, the axioms ∀xB (x) ⊃ B(y) and B(y) ⊃ ∃xB (x). A Kripke semantics is constructed for 2J and a completeness theorem is proven. A result of D. Gabbay is generalized concerning the undecidability of C2J+-extension of 2J by schemes ∃x (x ≡B) and ∀x(A ∀ B(x))⊃A ∀xB (x) specificially: the undecidability is proven of each T theory in language L such that [2J]⊑T ⊑[C2J+] ([2J] ([2J] denotes the set of all theorems of calculus 2J).

Related Organizations

Steklov Mathematical Institute
Russian Federation
Department of Mathematical Sciences
Russian Federation

Keywords

Categoricity and completeness of theories, Decidability of theories and sets of sentences, Logic with extra quantifiers and operators, intuitionistic propositional calculus with quantifiers, Other nonclassical logic, Intuitionistic mathematics, completeness theorem, Kripke-style semantics

Impact byBIP!

	citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	8
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 10%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average