This article is cited in 12 papers

On Hyperarithmetical Realizability

A. Yu. Konovalov, V. E. Plisko

Lomonosov Moscow State University

Abstract: The notion of hyperarithmetical realizability is introduced for various extensions of the language of formal arithmetic. The correctness of classical, intuitionistic, and basic logic with respect to the semantics based on hyperarithmetical realizability is studied.

Keywords: hyperarithmetical realizability, formal arithmetic, hyperarithmetical set, hyperarithmetical predicate, hyperarithmetical function, Gödel number, universal function.

UDC: 510.25+510.64

Received: 13.03.2015

DOI: 10.4213/mzm10735

 English version: Mathematical Notes, 2015, 98:5, 778–797

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