Geodesic
Basic Predicate Calculus is not Sound with Respect to the Strong Variant of Strictly Primitive Recursive Realizability
Matematičeskie zametki, Tome 111 (2022) no. 2, pp. 241-257 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that basic predicate calculus BQC is not sound with respect to the strong variant of strictly primitive recursive realizability.
Keywords: strictly primitive recursive realizability, basic predicate calculus BQC, constructive semantics, realizability. 
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A. Yu. Konovalov. Basic Predicate Calculus is not Sound with Respect to the Strong Variant of Strictly Primitive Recursive Realizability. Matematičeskie zametki, Tome 111 (2022) no. 2, pp. 241-257. http://geodesic.mathdoc.fr/item/MZM_2022_111_2_a6/

[1] S. Kleene, “On the interpretation of intuitionistic number theory”, J. Symbolic Logic, 10:4 (1945), 109–124 | DOI | Zbl

[2] Z. Damnjanovic, “Strictly primitive recursive realizability”, J. Symbolic Logic, 59:4 (1994), 1210-1227 | DOI | Zbl

[3] S. Salehi, “Provably total functions of basic arithmetic”, Math. Logic Quarterly, 49:3 (2003), 316–322 | DOI | Zbl

[4] Pak Ben Kha, Subrekursivnaya realizuemost i logika prekatov, Dis. kand. fiz.-matem. nauk, Mosk. un-t, M., 2003

[5] V. Plisko, Primitive Recursive Realizability and Basic Propositional Logic, Preprint 261, Utrecht Univ., 2007

[6] A. Visser, “A propositional logic with explicit fixed points”, Studia Logica, 40 (1981), 155–175 | DOI | Zbl

[7] W. Ruitenburg, “Basic predicate calculus”, Notre Dame J. Formal Logic, 39:1 (1998), 18-46 | DOI | Zbl

[8] A. Grzegorczyk, “Some classes of recursive functions”, Rozprawy Mat., 4 (1953), 1–46 | MR

[9] P. Axt, “Enumeration and the Grzegorczyk hierarchy”, Z. Math. Logik Grundlagen Math., 9 (1963), 53–65 | DOI | Zbl

[10] A. Yu. Konovalov, “$\Lambda$-Vyrazheniya dlya primitivno-rekursivnykh funktsii v ierarkhii Gzhegorchika”, Intellekt. sistemy. Teoriya i prilozh., 25:1 (2021), 97–114