## Limit Spaces and Transfinite Types (1998)

Citations: | 2 - 0 self |

### BibTeX

@TECHREPORT{Normann98limitspaces,

author = {Dag Normann and Geir Waagbø},

title = {Limit Spaces and Transfinite Types},

institution = {},

year = {1998}

}

### OpenURL

### 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.

### Citations

24 |
Filter spaces and continuous functionals
- Hyland
- 1979
(Show Context)
Citation Context ... 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... |

23 |
Recursion on the countable functionals
- Normann
- 1980
(Show Context)
Citation Context ... 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... |

12 |
Total sets and objects in domain theory, Annals of Pure and Applied Logic 60
- Berger
- 1993
(Show Context)
Citation Context ...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... |

9 | Continuous Functionals of Dependent and Transfinite Types
- Berger
- 1999
(Show Context)
Citation Context ...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... |

8 |
Semantics for some constructors of type theory
- Kristiansen, Normann
- 1995
(Show Context)
Citation Context ...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... |

6 |
The hereditarily partial effective functionals and recursion theory in higher types
- Longo, Moggi
- 1984
(Show Context)
Citation Context ...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... |

3 |
Topologie Vol 1, Warsawa
- Kuratowski
- 1952
(Show Context)
Citation Context ...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... |