A rich hierarchy of functionals of finite types

Dag Normann

doi:10.2168/LMCS-5(3:11)2009

Dag Normann - A rich hierarchy of functionals of finite types

lmcs:954 - Logical Methods in Computer Science, September 24, 2009, Volume 5, Issue 3 - https://doi.org/10.2168/LMCS-5(3:11)2009

A rich hierarchy of functionals of finite typesArticle

Authors: Dag Normann

We are considering typed hierarchies of total, continuous functionals using complete, separable metric spaces at the base types. We pay special attention to the so called Urysohn space constructed by P. Urysohn. One of the properties of the Urysohn space is that every other separable metric space can be isometrically embedded into it. We discuss why the Urysohn space may be considered as the universal model of possibly infinitary outputs of algorithms.
The main result is that all our typed hierarchies may be topologically embedded, type by type, into the corresponding hierarchy over the Urysohn space. As a preparation for this, we prove an effective density theorem that is also of independent interest.

Comment: 21 pages

https://doi.org/10.2168/LMCS-5(3:11)2009

Source: arXiv.org:0909.1198

Volume: Volume 5, Issue 3

Published on: September 24, 2009

Imported on: February 9, 2009

Keywords: Computer Science - Logic in Computer Science, F.1.1, F.4.1, F.3.2

Licence: arXiv.org - Non-exclusive license to distribute