“School of Mathematics”
Back to Papers HomeBack to Papers of School of Mathematics
| Paper IPM / M / 45 |
|
||||
| Abstract: | |||||
|
Buss asked in [1] whether every intuitionistic theory is, for some classical theory T, that of all T-normal Kripke structures H (T) for which he gave an r.e. axiomatization. In the language of
arithmetic Iop and Lop denote PA− plus Open Induction or Open LNP, iop and lop are their intuitionistic deductive closures. We show H (Iop)=lop is recursively axiomatizable and lop \vdashi c \dashv iop, while i∀1 \not\vdash lop. If iT proves
PEMatomic but not totality of a classically provably total Diophantine
function of T, then H(T) ⊄ eq i T and so iT ∉ range (H). A result due to Wehmeier then implies iΠ1 ∉ range (H). We prove Iop is not ∀2-conservative over i∀1. If Iop ⊆ T ⊆ I∀1, then iT is not closed under MRopen or Friedman's translation, so iT ∉ range (H). Both Iop and I∀1 are closed under the negative
translation.
Download TeX format |
|||||
| back to top | |||||
