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| Paper IPM / M / 2315 |
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| Abstract: | |
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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∃z Exp (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∃z Exp(x,y,z). Therefore, i∀1 \nvdash¬¬lop and iΠ1\nvdash ¬¬iΣ1. We also prove that HA\nvdashlΣ1 and present some remarks about iΠ2.
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