H-theories, fragments of HA and PA-normality

For a classical theory T, H(T) denotes the intuitionistic theory of T-normal (i.e. locally T) Kripke structures. S. Buss has asked for a characterization of the theories in the range of H and raised the particular question of whether HA is an H-theory. We show that Ti range(H) iff Ti = H(T). As a corollary, no fragment of HA extending i1 belongs to the range of H. A. Visser has already proved that HA is not in the range of H by different methods. We provide more examples of theories not in the range of H. We show PA-normality of once-branching Kripke models of HA + MP, where it is not known whether the same holds if MP is dropped. 1991 Mathematics Subject Classification: 03F55, 03F30. Key words and phrases: Friedman's Translation, T-normal Kripke structures, Heyting Arithmetic, Markov's Principle. 0. Preliminaries We fix the language {+,

• Type: Journal
• Year: 2002
• Where: AML
• Authors: Morteza Moniri
• Keywords: AML 2002, Intuitionistic Theory, Kripke Structures, Once-branching Kripke Models