کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6424782 | 1633473 | 2013 | 17 صفحه PDF | دانلود رایگان |

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]=ãfξãξâOn, called its hyperation, in such a way that f0=id, f1=f and fα+β=fαâfβ 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]=ãgξãξâOn, which is a family of initial functions such that gξ is a left adjoint to fξ for all ξ.
Journal: Annals of Pure and Applied Logic - Volume 164, Issues 7â8, August 2013, Pages 785-801