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Paper   IPM / M / 2315
School of Mathematics
  Title:   Intuitionistic weak arithmetic
  Author(s):  Mor. Moniri
  Status:   Published
  Journal: Arch. Math. Logic
  Vol.:  42
  Year:  2003
  Pages:   791-796
  Supported by:  IPM
We construct ω-framed Kripke models of i1 and iΠ1 non of whose worlds satisfies ∀xy(x=2yx=2y+1) and ∀x,yz Exp (x,y,z) respectively. This will enable us to show that i1 does not prove ¬¬∀xy (x=2yx=2y+1) and iΠ1 does not prove ¬¬∀x,yz Exp(x,y,z). Therefore, i1 \nvdash¬¬lop and iΠ1\nvdash ¬¬iΣ1. We also prove that HA\nvdashlΣ1 and present some remarks about iΠ2.

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