$\Sigma_n$-bounding and $\Delta_n$-induction
نویسندگان
چکیده
منابع مشابه
Σn-BOUNDING AND ∆n-INDUCTION
Working in the base theory of PA−+ IΣ0 + exp, we show that for all n ∈ ω, the bounding principle for Σn-formulas (BΣn) is equivalent to the induction principle for ∆n-formulas (I∆n). This partially answers a question of J. Paris.
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Working in the base theory of PA + I60 + exp, we show that for all n ∈ ω, the bounding principle for 6n-formulas (B6n) is equivalent to the induction principle for 1n-formulas (I1n). This partially answers a question of J. Paris; see Clote and Krajı́ček (1993).
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2004
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-04-07294-6