A rich hierarchy of functionals of finite types

Details A rich hierarchy of functionals of finite types A rich hierarchy of functionals of finite types

2009-09-07

arxiv.org/abs/0909.1198v2

LMCS 5 (3:11) 2009

Computer Science

Logic in Computer Science

21 pages

Scientific paper

10.2168/LMCS-5(3:11)2009

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.

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