“School of Mathematics”
Back to Papers HomeBack to Papers of School of Mathematics
Paper IPM / M / 634  


Abstract:  
In the first section of this paper we show that iΠ_{1} ≡ W¬¬lΠ_{1} and that a Kripke model which decides bounded formulas forces iΠ_{1} if and only if the union of the worlds in any path in it satisfies IΠ_{1}. In particular, the union of the worlds in any path of a Kripke model
of HA models IΠ_{1}. In the second section of the paper, we show that for equivalence of forcing and satisfaction of
Π_{m}formulas in a linear Kripke model deciding ∆_{0}formulas, it is necessary and sufficient that the model be Σ_{m}elementary. This implies that if a linear Kripke model forces PEM_{prenex}, then it forces PEM. We also show that, for each n\geqslant 1, iΦ_{n} does not prove H(IΠ_{n}). Here, Φ_{n}'s are Burr's fragments
of HA.
Download TeX format 

back to top 