@TECHREPORT{Normann98limitspaces, author = {Dag Normann and Geir Waagbø}, title = {Limit Spaces and Transfinite Types}, institution = {}, year = {1998} }

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Abstract

We give a characterisation of an extension of the Kleene-Kreisel continuous functionals to objects of transfinite types using limit spaces of transfinite types.

... of continuous functionals; we call these continuous functionals of transfinite type and consider this as a natural extension of the notion of continuous functionals of finite type as studied in e.g. =-=[4, 8, 10]-=-. The purpose of the present paper is to provide a topological characterisation of these functionals. For the continuous functionals of finite type a characterisation using limit spaces has been given...

... of continuous functionals; we call these continuous functionals of transfinite type and consider this as a natural extension of the notion of continuous functionals of finite type as studied in e.g. =-=[4, 8, 10]-=-. The purpose of the present paper is to provide a topological characterisation of these functionals. For the continuous functionals of finite type a characterisation using limit spaces has been given...

...of transfinite types. I Introduction The theory of (Scott-Ershov) domains with totality has evolved in the last few years through a number of papers by Normann (and Kristiansen) [5, 9, 11] and Berger =-=[1, 2]-=-. One source of inspiration for this theory is MartinL6f 's type theory, and in [18] it is shown how the theory of domains with totality can be used to construct semantics for this type theory; recall...

...of transfinite types. I Introduction The theory of (Scott-Ershov) domains with totality has evolved in the last few years through a number of papers by Normann (and Kristiansen) [5, 9, 11] and Berger =-=[1, 2]-=-. One source of inspiration for this theory is MartinL6f 's type theory, and in [18] it is shown how the theory of domains with totality can be used to construct semantics for this type theory; recall...

...es using limit spaces of transfinite types. I Introduction The theory of (Scott-Ershov) domains with totality has evolved in the last few years through a number of papers by Normann (and Kristiansen) =-=[5, 9, 11]-=- and Berger [1, 2]. One source of inspiration for this theory is MartinL6f 's type theory, and in [18] it is shown how the theory of domains with totality can be used to construct semantics for this t...

...f (x)) whenever (t',y)s(s',x).sandscorrespond o extensional cqualiW, and ha every time,ion-like oal objec of his hierarchy is extensional. In he proof we exend a method of proof due o Longo and Moggi =-=[7]-=- o ransfinic ypcs. Definition 8 By ransfinie recursion we now consruc he set of types T, he interpretation Tp(t) for each t C T as he image of he collapsing ion p : SwfsT and hc collapsing time,ions p...

...ce is systematically avoided. 2 Limit Spaces 2.1 Basic definitions We let a limit space be a set with a notion of convergency satisfying three properties. We have taken our definition from Kuratowski =-=[6]-=-, where we use the following notation: In a sequence {Xn}n_ we will identify 'no index' with 'index '. In this context, x, or simply x, will be called the alleged limit. Definition I Let X be a set. A...