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IPM
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“School of Mathematics”

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Paper   IPM / M / 770
School of Mathematics
  Title:   Independence results for weak systems of intuitionistic arithmetic
  Author(s):  Mor. Moniri
  Status:   Published
  Journal: Math. Logic Quart.
  No.:  3
  Vol.:  49
  Year:  2003
  Pages:   250-254
  Supported by:  IPM
  Abstract:
This paper proves some independence results for weak fragments of Heyting arithmetic by using Kripke models. We present a necessary condition for linear Kripke models of arithmetical theories which are closed under the negative translation and use it to show that the union of the worlds in any linear Kripke model of HA satisfies PA. We construct a two-node PA-normal Kripke structure which does not force iΣ2. We prove i1\nvdash i1, i1\nvdashi1, iΠ2\nvdash iΣ2 and iΣ2\nvdashiΠ2. We use Smorynski's operation Σ to show HA\nvdash lΠ1.

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