A rich hierarchy of functionals of finite types
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 ca...
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| Format: | Article |
| Language: | English |
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Logical Methods in Computer Science e.V.
2009-09-01
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| Series: | Logical Methods in Computer Science |
| Subjects: | |
| Online Access: | https://lmcs.episciences.org/954/pdf |
| _version_ | 1827322909283057664 |
|---|---|
| author | Dag Normann |
| author_facet | Dag Normann |
| author_sort | Dag Normann |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-25T01:37:22Z |
| format | Article |
| id | doaj.art-1b7b729952c847c8bd9e1c1fcd8ea52e |
| institution | Directory Open Access Journal |
| issn | 1860-5974 |
| language | English |
| last_indexed | 2024-04-25T01:37:22Z |
| publishDate | 2009-09-01 |
| publisher | Logical Methods in Computer Science e.V. |
| record_format | Article |
| series | Logical Methods in Computer Science |
| spelling | doaj.art-1b7b729952c847c8bd9e1c1fcd8ea52e2024-03-08T09:01:29ZengLogical Methods in Computer Science e.V.Logical Methods in Computer Science1860-59742009-09-01Volume 5, Issue 310.2168/LMCS-5(3:11)2009954A rich hierarchy of functionals of finite typesDag NormannWe 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.https://lmcs.episciences.org/954/pdfcomputer science - logic in computer sciencef.1.1f.4.1f.3.2 |
| spellingShingle | Dag Normann A rich hierarchy of functionals of finite types Logical Methods in Computer Science computer science - logic in computer science f.1.1 f.4.1 f.3.2 |
| title | A rich hierarchy of functionals of finite types |
| title_full | A rich hierarchy of functionals of finite types |
| title_fullStr | A rich hierarchy of functionals of finite types |
| title_full_unstemmed | A rich hierarchy of functionals of finite types |
| title_short | A rich hierarchy of functionals of finite types |
| title_sort | rich hierarchy of functionals of finite types |
| topic | computer science - logic in computer science f.1.1 f.4.1 f.3.2 |
| url | https://lmcs.episciences.org/954/pdf |
| work_keys_str_mv | AT dagnormann arichhierarchyoffunctionalsoffinitetypes AT dagnormann richhierarchyoffunctionalsoffinitetypes |