Degree Spectra of Relations on a Cone

Let \mathcal A be a mathematical structure with an additional relation R. The author is interested in the degree spectrum of R, either among computable copies of \mathcal A when (\mathcal A,R) is a "natural" structure, or (to make this rigorous) among copies of (\mathcal A,R) computable in...

Full description

Saved in:
Bibliographic Details
Main Author: Harrison-Trainor, Matthew
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 2018
Edition:1
Series:Memoirs of the American Mathematical Society
Subjects:
Angles (Geometry)
Angles (Geometry) > Measurement
Conic sections
Unsolvability (Mathematical logic)
degree spectrum of a relation
cone of Turing degrees
computable structure
ISBN:1470428393, 9781470428396
ISSN:0065-9266, 1947-6221
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract Let \mathcal A be a mathematical structure with an additional relation R. The author is interested in the degree spectrum of R, either among computable copies of \mathcal A when (\mathcal A,R) is a "natural" structure, or (to make this rigorous) among copies of (\mathcal A,R) computable in a large degree d. He introduces the partial order of degree spectra on a cone and begin the study of these objects. Using a result of Harizanov--that, assuming an effectiveness condition on \mathcal A and R, if R is not intrinsically computable, then its degree spectrum contains all c.e. degrees--the author shows that there is a minimal non-trivial degree spectrum on a cone, consisting of the c.e. degrees.
AbstractList Let
Let $\mathcal A$ be a mathematical structure with an additional relation $R$. The author is interested in the degree spectrum of $R$, either among computable copies of $\mathcal A$ when $(\mathcal A,R)$ is a ``natural'' structure, or (to make this rigorous) among copies of $(\mathcal A,R)$ computable in a large degree d. He introduces the partial order of degree spectra on a cone and begin the study of these objects. Using a result of Harizanov--that, assuming an effectiveness condition on $\mathcal A$ and $R$, if $R$ is not intrinsically computable, then its degree spectrum contains all c.e. degrees--the author shows that there is a minimal non-trivial degree spectrum on a cone, consisting of the c.e. degrees.
Author Harrison-Trainor, Matthew
Author_xml – sequence: 1
  fullname: Harrison-Trainor, Matthew
BackLink https://cir.nii.ac.jp/crid/1130282272750515456$$DView record in CiNii
BookMark eNpVkctOwzAQRQ20iLZ0wR9EAoRYhI7f9hJKeUiVkACxtZzEhtA0LnWA3ydpu2Ezs5ijuTP3DlGvDrVD6ATDFQYNk6VbhgkmoPbQWEuFmQTGGMZkHw2wZjIVhOADNNwMiKKa9tAAQPBUEyH6aEgAK8CScnbYUkAVSKWVOELDGD8BQAGTA3R-697XziUvK5c3a5sEnzy7yjZlqGMS6sQm0_auY9T3topuvOsj9HY3e50-pPOn-8fp9Ty1lBKsU0pFIYktZC6oExkQyKmXztJCcC2zzBFfFLY9F7TPVK6wz5X3XiumZF54TkfocrvYxoX7jR-haqL5qVwWwiKafz607MWWXa3D17eLjdlguavbRyozu5lyBro1oSXPtmRdliYvu4oxBaIIkURy4JgzLlrsdCe-jGYnicF0cZguDtPFQf8AlCdvaw
ContentType eBook
Book
Copyright Copyright 2018 American Mathematical Society
Copyright_xml – notice: Copyright 2018 American Mathematical Society
DBID RYH
DEWEY 511.3
DOI 10.1090/memo/1208
DatabaseName CiNii Complete
DatabaseTitleList


DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISBN 9781470444112
1470444119
EISSN 1947-6221
Edition 1
ExternalDocumentID 9781470444112
EBC5409180
BB26311572
10_1090_memo_1208
GroupedDBID --Z
-~X
123
4.4
85S
ABPPZ
ACNCT
ACNUO
AEGFZ
AENEX
ALMA_UNASSIGNED_HOLDINGS
DU5
P2P
RMA
WH7
YNT
YQT
3.E
38.
AABBV
AAWPO
ABARN
ABQPQ
ACLGV
ADVEM
AEKGI
AERYV
AFOJC
AHWGJ
AJFER
AZNFR
AZZ
BBABE
CZZ
GEOUK
RYH
ID FETCH-LOGICAL-a33219-336d72ad7c63e6b020c3f7ea3d6597bbe2fdda42809fb8c81fc8fff98487cdf53
ISBN 1470428393
9781470428396
ISICitedReferencesCount 3
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=0000055994&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0065-9266
IngestDate Fri Nov 08 04:33:09 EST 2024
Wed Dec 10 12:01:44 EST 2025
Thu Jun 26 23:35:11 EDT 2025
Thu Aug 14 15:25:36 EDT 2025
IsPeerReviewed true
IsScholarly true
Keywords degree spectrum of a relation
cone of Turing degrees
computable structure
LCCN 2018017354
LCCallNum_Ident QA9.63 .H377 2018
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-a33219-336d72ad7c63e6b020c3f7ea3d6597bbe2fdda42809fb8c81fc8fff98487cdf53
Notes Includes bibliographical references and index
May 2018, volume 253, number 1208 (third of 7 numbers)
OCLC 1038078986
PQID EBC5409180
PageCount 120
ParticipantIDs askewsholts_vlebooks_9781470444112
proquest_ebookcentral_EBC5409180
nii_cinii_1130282272750515456
ams_ebooks_10_1090_memo_1208
PublicationCentury 2000
PublicationDate [2018]
PublicationDateYYYYMMDD 2018-01-01
PublicationDate_xml – year: 2018
  text: [2018]
PublicationDecade 2010
PublicationPlace Providence, Rhode Island
PublicationPlace_xml – name: Providence, Rhode Island
– name: Providence, RI
– name: Providence
PublicationSeriesTitle Memoirs of the American Mathematical Society
PublicationYear 2018
Publisher American Mathematical Society
Publisher_xml – name: American Mathematical Society
SSID ssj0008047
ssj0002007189
Score 2.667105
Snippet Let
Let \mathcal A be a mathematical structure with an additional relation R. The author is interested in the degree spectrum of R, either among computable copies...
Let $\mathcal A$ be a mathematical structure with an additional relation $R$. The author is interested in the degree spectrum of $R$, either among computable...
SourceID askewsholts
proquest
nii
ams
SourceType Aggregation Database
Publisher
SubjectTerms Angles (Geometry)
Angles (Geometry) -- Measurement
Conic sections
Unsolvability (Mathematical logic)
TableOfContents Introduction -- Preliminaries -- Degree Spectra between the C.E. Degrees and the D.C.E. Degrees -- Degree Spectra of Relations on the Naturals -- A “Fullness” Theorem for 2-CEA\xspace Degrees -- Further Questions -- Relativizing Harizanov’s Theorem on C.E. Degrees
Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Preliminaries -- 2.1. Computability Theory -- 2.2. Computable Structure Theory -- 2.3. Relativizing to a Cone -- Chapter 3. Degree Spectra between the C.E. Degrees and the D.C.E. Degrees -- 3.1. Necessary and Sufficient Conditions to be Intrinsically of C.E. Degree -- 3.2. Incomparable Degree Spectra of D.C.E. Degrees -- Chapter 4. Degree Spectra of Relations on the Naturals -- Chapter 5. A "Fullness" Theorem for 2-\cea Degrees -- 5.1. Approximating a 2-\cea Set -- 5.2. Basic Framework of the Construction -- 5.3. An Informal Description of the Construction -- 5.4. The Game Gs and the Final Condition -- 5.5. Basic Plays and the Basic Game -- 5.6. The Construction -- Chapter 6. Further Questions -- Appendix A. Relativizing Harizanov's Theorem on C.E. Degrees -- A.1. Framework of the Proof -- A.2. The First Two Cases -- A.3. The Third Case -- Bibliography -- Index of Notation and Terminology -- Back Cover
Title Degree Spectra of Relations on a Cone
URI https://www.ams.org/memo/1208/
https://cir.nii.ac.jp/crid/1130282272750515456
https://ebookcentral.proquest.com/lib/[SITE_ID]/detail.action?docID=5409180
https://www.vlebooks.com/vleweb/product/openreader?id=none&isbn=9781470444112
Volume 253
WOSCitedRecordID wos0000055994&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9QwEB7RhQN74ikWWhQhOKGoib3rx3XLQiVQ4bCg3iLHD2lFm6BkqfrzmXFeVXtAHLhYiRV55G8ce2Y8D4C33JUOtWSTMqFsujRlmeplkKnlguwMTuc2Vi35Is_O1Pm5_taXlmxjOQFZVer6Wv_6r6zGPmQ2hc7-A7vHQbEDn5Hp2CLbsb0lEY-vHcc_eNSd_fsYO9kYkgKbydOtoijIerpDPzVNrD6YbqlGRKez97W_bxoCcnXLEDDd8Iz5XimfSD0mFBm1xnwpSVPiXSnZO3topsnp8NJf1qTVs0xNR8XowLdeMxHz9ODpdyAFar33P22-fv88mrfIBJorHUPpemp8yLA1UB8SPensmKgdE62Y8Ladw9y0P3GXxxNgj28H1W5357CMEsD2EcwoKuQx3PPVE5hPk2-fwrsO-KQHPqlDMgKf1FViEgL-Gfz4uNmenKZ99YnUcI77eMq5cJIZJ63gXpQ4JcuD9IY7gVpYWXoWnDM4lUyHUlmVB6tCCFqhDmhdWPHnMKtw_BeQlAH_BObVikm2XFmpnLdCKBOcDTJIuYBDnHUR78fbovMLyAoCpSBQFvDmBhzF1UX_4YAmirQ5W8ARolTYHbU53Uej7Ccpff8qiskLSAb8OkK992-xWZ-g2K5zlb38yxCv4OG08A5htm9--yN4YK_2u7Z53S-BP6jTMIc
linkProvider ProQuest Ebooks
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.title=Degree+spectra+of+relations+on+a+cone&rft.au=Harrison-Trainor%2C+Matthew&rft.date=2018-01-01&rft.pub=American+Mathematical+Society&rft.isbn=9781470428396&rft_id=info:doi/10.1090%2Fmemo%2F1208&rft.externalDocID=BB26311572
thumbnail_m http://cvtisr.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Fvle.dmmserver.com%2Fmedia%2F640%2F97814704%2F9781470444112.jpg