Inductive definitions over a predicative arithmetic
نویسندگان
چکیده
منابع مشابه
Forcing for hat inductive definitions in arithmetic
By forcing, we give a direct interpretation of ÎDω into Avigad’s FP. To the best of the author’s knowledge, this is one of the simplest applications of forcing to “real problems”.
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We give a simple proof of a theorem of Gurevich and Shelah, that the inductive closure of an inflationary operator is equivalent, over the class of finite structures, to the inductive closure (i.e. minimal fixpoint) of a positive operator. A variant of the same proof establishes a theorem of Immerman, that the class of inductive closures of positive first order operators is closed under complem...
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Predicative mathematics in the sense originating with Poincaré and Weyl begins by taking the natural number system for granted, proceeding immediately to real analysis and related fields. On the other hand, from a logicist or set-theoretic standpoint, this appears problematic, for, as the story is usually told, impredicative principles seem to play an essential role in the foundations of arithm...
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A fragment with the same provably recursive functions as n iterated inductive definitions is obtained by restricting second order arithmetic in the following way. The underlying language allows only up to n + 1 nested second order quantifications and those are in such a way, that no second order variable occurs free in the scope of another second order quantifier. The amount of induction on ari...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2005
ISSN: 0168-0072
DOI: 10.1016/j.apal.2005.05.011