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Intuitionistic weak arithmetic

Intuitionistic weak arithmetic We construct ω-framed Kripke models of i∀1 and iΠ1 non of whose worlds satisfies ∀x∃y(x=2y∨x=2y+1) and ∀x,y∃zExp(x, y, z) respectively. This will enable us to show that i∀1 does not prove ¬¬∀x∃y(x=2y∨x=2y+1) and iΠ1 does not prove ¬¬∀x, y∃zExp(x, y, z). Therefore, i∀1⊬¬¬lop and iΠ1⊬¬¬iΣ1. We also prove that HA⊬lΣ1 and present some remarks about iΠ2. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

Intuitionistic weak arithmetic

Moniri, Morteza
Archive for Mathematical Logic , Volume 42 (8) – May 16, 2003
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References (16)

Publisher
Springer Journals
Copyright
Copyright © 2003 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/s00153-003-0189-8
Publisher site
See Article on Publisher Site

Abstract

We construct ω-framed Kripke models of i∀1 and iΠ1 non of whose worlds satisfies ∀x∃y(x=2y∨x=2y+1) and ∀x,y∃zExp(x, y, z) respectively. This will enable us to show that i∀1 does not prove ¬¬∀x∃y(x=2y∨x=2y+1) and iΠ1 does not prove ¬¬∀x, y∃zExp(x, y, z). Therefore, i∀1⊬¬¬lop and iΠ1⊬¬¬iΣ1. We also prove that HA⊬lΣ1 and present some remarks about iΠ2.

Journal

Archive for Mathematical Logic – Springer Journals

Published: May 16, 2003

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