Independence results for weak systems of intuitionistic arithmetic Export

@article{citeulike:3359038, 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 iSigma2. We prove iforall1 \⊬ iexist1, iexist1 \⊬ iforall1, iPi2 \⊬ iSigma2 and iSigma2 \⊬ iPi2. We use Smorynski's operation Sigmaprime to show HA \⊬ lPi1.}, address = {Institute for Studies in Theoretical Physics and Mathematics (IPM), P.O. Box 19395-5746, Tehran, Iran}, author = {Moniri, Morteza}, citeulike-article-id = {3359038}, citeulike-linkout-0 = {http://dx.doi.org/10.1002/malq.200310024}, citeulike-linkout-1 = {http://www3.interscience.wiley.com/cgi-bin/abstract/103520656/ABSTRACT}, doi = {10.1002/malq.200310024}, journal = {MLQ}, keywords = {bounded-arithmetic, constructive-mathematics, kripke-model}, number = {3}, pages = {250--254}, posted-at = {2008-09-30 15:51:17}, priority = {2}, title = {Independence results for weak systems of intuitionistic arithmetic}, url = {http://dx.doi.org/10.1002/malq.200310024}, volume = {49}, year = {2003} }

TY - JOUR ID - citeulike:3359038 L3 - citeulike-article-id:3359038 N2 - 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 iSigma2. We prove iforall1 ⊬ iexist1, iexist1 ⊬ iforall1, iPi2 ⊬ iSigma2 and iSigma2 ⊬ iPi2. We use Smorynski's operation Sigmaprime to show HA ⊬ lPi1. IS - 3 JF - MLQ AD - Institute for Studies in Theoretical Physics and Mathematics (IPM), P.O. Box 19395-5746, Tehran, Iran EP - 254 TI - Independence results for weak systems of intuitionistic arithmetic VL - 49 SP - 250 KW - bounded-arithmetic KW - constructive-mathematics KW - kripke-model AU - Moniri, Morteza PY - 2003/// UR - http://dx.doi.org/10.1002/malq.200310024 ER -