Intuitionistic weak arithmetic |
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| Authors: | Email author" target="_blank">Morteza?MoniriEmail author |
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| Institution: | (1) Institute for Studies in Theoretical Physics and Mathematics (IPM), P.O. Box 19395-5746, Tehran, Iran;(2) Department of Mathematics, Shahid Beheshti University, Tehtan, Irau |
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| Abstract: | We construct  -framed Kripke models of i 1 and i 1 non of whose worlds satisfies x y(x=2y x=2y+1) and x,yzExp(x, y, z) respectively. This will enable us to show that i1 does not prove ¬¬xy(x=2yx=2y+1) and i1 does not prove ¬¬x, yzExp(x, y, z). Therefore, i1 ¬¬lop and i1¬¬i 1. We also prove that HAl1 and present some remarks about i2.
Mathematics Subject Classification (2000): 03F30, 03F55, 03H15. |
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| Keywords: | Fragments of Heyting Arithmetic Kripke Models exp |
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