Arithmetic transfinite induction and recursive well-orderings
نویسندگان
چکیده
منابع مشابه
Transfinite Induction within Peano Arithmetic
The relative strengths of first-order theories axiomatized by transfinite induction, for ordinals less-than ~0, and formulas restricted in quantifier complexity, is determined. This is done, in part, by describing the provably recursive functions of such theories. Upper bounds for the provably recursive functions are obtained using model-theoretic techniques. A variety of additional results tha...
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Ordinal notations and provability of well-foundedness have been a central tool in the study of the consistency strength and computational strength of formal theories of arithmetic. This development began with Gentzen’s consistency proof for Peano arithmetic based on the well-foundedness of ordinal notations up to ǫ0. Since the work of Gentzen, ordinal notations and provable wellfoundedness have...
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ATR0 is the natural subsystem of second-order arithmetic in which one can develop a decent theory of ordinals. We investigate classes of structures which are in a sense the “well-founded part” of a larger, simpler class, for example, superatomic Boolean algebras (within the class of all Boolean algebras). The other classes we study are: well-founded trees, reduced Abelian p-groups, and countabl...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1985
ISSN: 0001-8708
DOI: 10.1016/0001-8708(85)90036-2