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IPM
30
YEARS OLD

“School of Mathematics”

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Paper   IPM / M / 528
School of Mathematics
  Title:   H-theories, fragments of HA and PA-normality
  Author(s):  Mor. Moniri
  Status:   Published
  Journal: Arch. Math. Logic
  No.:  1
  Vol.:  41
  Year:  2002
  Pages:   101-105
  Publisher(s):   Springer
  Supported by:  IPM
  Abstract:
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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