Classes of Polish Spaces under Effective Borel Isomorphism. (Record no. 127890)
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| 000 -LEADER | |
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| fixed length control field | 03719nam a22004693i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC4901854 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240729131324.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2016 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470428228 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781470415631 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC4901854 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL4901854 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)938446269 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA611.28 .G74 2015 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 511.3/22 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Gregoriades, Vassilios. |
| 245 10 - TITLE STATEMENT | |
| Title | Classes of Polish Spaces under Effective Borel Isomorphism. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2016. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2015. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (102 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society Series ; |
| Volume/sequential designation | v.240 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover -- Title page -- Preface -- Chapter 1. Introduction -- 1.1. A few words about the setting -- 1.2. The basic notions -- 1.3. Theorems in the general context -- 1.4. The Cantor-Bendixson decomposition -- Chapter 2. The spaces \spat{T} -- 2.1. Definition and properties -- 2.2. Elementary facts about the classes of \del isomorphism -- Chapter 3. Kleene spaces -- 3.1. Definition and basic properties -- 3.2. Expanding the toolbox -- 3.3. Chains and antichains in Kleene spaces under \dleq -- 3.4. Analogy with recursive pseudo-well-orderings -- 3.5. Incomparable hyperdegrees in Kleene spaces -- Chapter 4. Characterizations of \ca{N} up to \del isomorphism -- 4.1. Copies of the complete binary tree -- 4.2. A characterization in terms of the perfect kernel -- 4.3. A measure-theoretic characterization -- 4.4. The tree of attempted embeddings -- Chapter 5. Spector-Gandy spaces -- 5.1. The Spector-Gandy Theorem -- 5.2. Application to the spaces \spat{T} -- 5.3. Chains and antichains in Spector-Gandy spaces under \dleq -- Chapter 6. Questions and related results -- 6.1. Parametrization -- 6.2. Kleene spaces -- 6.3. Incomparable and minimal hyperdegrees -- 6.4. Connections with lattice theory -- 6.5. Attempted Embeddings and incomparability -- 6.6. Spector-Gandy spaces -- 6.7. Connections with \pii equivalence relations -- Bibliography -- Index -- Back Cover. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | The author studies the equivalence classes under \Delta^1_1 isomorphism, otherwise effective Borel isomorphism, between complete separable metric spaces which admit a recursive presentation and he shows the existence of strictly increasing and strictly decreasing sequences as well as of infinite antichains under the natural notion of \Delta^1_1-reduction, as opposed to the non-effective case, where only two such classes exist, the one of the Baire space and the one of the naturals. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Polish spaces (Mathematics). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Metric spaces. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Isomorphisms (Mathematics). |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Gregoriades, Vassilios |
| Title | Classes of Polish Spaces under Effective Borel Isomorphism |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2016 |
| International Standard Book Number | 9781470415631 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society Series |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4901854">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4901854</a> |
| Public note | Click to View |
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