Independence problems in subsystems of intuitionistic arithmetic
نویسندگان
چکیده
منابع مشابه
An Independence Result for Intuitionistic Bounded Arithmetic
It is shown that the intuitionistic theory of polynomial induction on positive Π1 (coNP) formulas does not prove the sentence ¬¬∀x, y∃z ≤ y(x ≤ |y| → x = |z|). This implies the unprovability of the scheme ¬¬PIND(Σ 1 ) in the mentioned theory. However, this theory contains the sentence ∀x, y¬¬∃z ≤ y(x ≤ |y| → x = |z|). The above independence result is proved by constructing an ω-chain of submode...
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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∃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 0 ¬¬lop and iΠ1 0 ¬¬iΣ1. We also prove that HA 0 lΣ1 and present some remarks about iΠ2. 2000 Mathematics Subject C...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae (Proceedings)
سال: 1971
ISSN: 1385-7258
DOI: 10.1016/s1385-7258(71)80052-5