“School of Mathematics”
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| Paper IPM / M / 528 |
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| Abstract: | |
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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 iΠ1 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.
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