2022/09/22 by V. E. Plisko, Plisko, V. E.
Computer Science · #03F65 #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge
paper · pdf · doi:10.48550/arxiv.2209.10940
openalex publication_date 2022/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Constructive arithmetic, or the Markov arithmetic MA, is obtained from intuitionistic arithmetic HA by adding the following two principles: the Markov principle M which distinguishes constructivism from intuitionism, and the so-called extended Church thesis ECT, which distinguishes constructive semantics from classical semantics. The first principle is expressed by a predicate formula, but ECT is formulated as a scheme in the arithmetical language. Some earlier results of the authors make possible to replace the scheme ECT by a pure predicate formula. This gives a predicate calculus MQC which can serve as a logical basis for constructive arithmetic. Namely, arithmetical theory based on MQC and Peano axioms proves all formulas deducible in MA. Note that MQC is not an intermediate calculus between intuitionistic and classical logics: it proves some formulas that are not deducible in the classical predicate calculus. Bibliography: 12 items.