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Paper   IPM / M / 2295
School of Mathematics
  Title:   On two questions about feasibly Constructive Arithmetic
  Author(s):  Mor. Moniri
  Status:   Published
  Journal: Math. Logic Quart.
  No.:  4
  Vol.:  49
  Year:  2003
  Pages:   425-427
  Supported by:  IPM
IPV is the intuitionistic theory axiomatized by Cook's equational theory PV plus PIND on NP-formulas. Two extensions of IPV were introduced by Buss and by Cook and Urquhart by adding PIND for formulas of the form A(x)∨B, respectively ¬¬A(x), where A(x) is NP and x is not free in B. Cook and Urquhart posed the question of whether these extensions are proper. We show that in each of the two cases the extension is proper unless the polynomial hierarchy collapses.

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