کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6424782 1633473 2013 17 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Hyperations, Veblen progressions and transfinite iteration of ordinal functions
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
پیش نمایش صفحه اول مقاله
Hyperations, Veblen progressions and transfinite iteration of ordinal functions
چکیده انگلیسی

Ordinal functions may be iterated transfinitely in a natural way by taking pointwise limits at limit stages. However, this has disadvantages, especially when working in the class of normal functions, as pointwise limits do not preserve normality. To this end we present an alternative method to assign to each normal function f a family of normal functions Hyp[f]=〈fξ〉ξ∈On, called its hyperation, in such a way that f0=id, f1=f and fα+β=fα∘fβ for all α, β.Hyperations are a refinement of the Veblen hierarchy of f. Moreover, if f is normal and has a well-behaved left-inverse g called a left adjoint, then g can be assigned a cohyperation coH[g]=〈gξ〉ξ∈On, which is a family of initial functions such that gξ is a left adjoint to fξ for all ξ.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 164, Issues 7–8, August 2013, Pages 785-801
نویسندگان
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