“School of Mathematics”

Back to Papers Home
Back to Papers of School of Mathematics

Paper   IPM / M / 634
School of Mathematics
  Title:   Weak arithmetics and Kripke models
  Author(s):  Mor. Moniri
  Status:   Published
  Journal: Math. Logic Quart.
  No.:  1
  Vol.:  48
  Year:  2002
  Pages:   157--160
  Publisher(s):   WILEY-VCH
  Supported by:  IPM
In the first section of this paper we show that iΠ1W¬¬lΠ1 and that a Kripke model which decides bounded formulas forces iΠ1 if and only if the union of the worlds in any path in it satisfies IΠ1. In particular, the union of the worlds in any path of a Kripke model of HA models IΠ1. In the second section of the paper, we show that for equivalence of forcing and satisfaction of Πm-formulas in a linear Kripke model deciding ∆0-formulas, it is necessary and sufficient that the model be Σm-elementary. This implies that if a linear Kripke model forces PEMprenex, then it forces PEM. We also show that, for each n\geqslant 1, iΦn does not prove H(IΠn). Here, Φn's are Burr's fragments of HA.

Download TeX format
back to top
scroll left or right