On a problem of Ishmukhametov
Given a d.c.e. degree d , consider the d.c.e. sets in d and the corresponding degrees of their Lachlan sets. Ishmukhametov provided a systematic investigation of such degrees, and proved that for a given d.c.e. degree d > 0 , the class of its c.e. predecessors in which d is c.e., denoted as R [d]...
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| Veröffentlicht in: | Archive for mathematical logic 2013-11, Vol.52 (7-8), p.733-741 |
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| container_title | Archive for mathematical logic |
| container_volume | 52 |
| creator | Fang, Chengling Wu, Guohua Yamaleev, Mars |
| description | Given a d.c.e. degree
d
, consider the d.c.e. sets in
d
and the corresponding degrees of their Lachlan sets. Ishmukhametov provided a systematic investigation of such degrees, and proved that for a given d.c.e. degree
d
>
0
, the class of its c.e. predecessors in which
d
is c.e., denoted as R
[d]
, can consist of either just one element, or an interval of c.e. degrees. After this, Ishmukhametov asked whether there exists a d.c.e. degree d for which the class R[d] has no minimal element. We give a positive answer to this question. |
| doi_str_mv | 10.1007/s00153-013-0340-0 |
| format | Article |
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d
, consider the d.c.e. sets in
d
and the corresponding degrees of their Lachlan sets. Ishmukhametov provided a systematic investigation of such degrees, and proved that for a given d.c.e. degree
d
>
0
, the class of its c.e. predecessors in which
d
is c.e., denoted as R
[d]
, can consist of either just one element, or an interval of c.e. degrees. After this, Ishmukhametov asked whether there exists a d.c.e. degree d for which the class R[d] has no minimal element. We give a positive answer to this question.</description><identifier>ISSN: 0933-5846</identifier><identifier>EISSN: 1432-0665</identifier><identifier>DOI: 10.1007/s00153-013-0340-0</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Algebra ; Mathematical analysis ; Mathematical Logic and Foundations ; Mathematical problems ; Mathematics ; Mathematics and Statistics ; Theorems</subject><ispartof>Archive for mathematical logic, 2013-11, Vol.52 (7-8), p.733-741</ispartof><rights>Springer-Verlag Berlin Heidelberg 2013</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-b90bb85749a9041c8f34bfed1054fe2792c8318aa4e7423f575b933c5b6d303a3</citedby><cites>FETCH-LOGICAL-c316t-b90bb85749a9041c8f34bfed1054fe2792c8318aa4e7423f575b933c5b6d303a3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00153-013-0340-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00153-013-0340-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27915,27916,41479,42548,51310</link.rule.ids></links><search><creatorcontrib>Fang, Chengling</creatorcontrib><creatorcontrib>Wu, Guohua</creatorcontrib><creatorcontrib>Yamaleev, Mars</creatorcontrib><title>On a problem of Ishmukhametov</title><title>Archive for mathematical logic</title><addtitle>Arch. Math. Logic</addtitle><description>Given a d.c.e. degree
d
, consider the d.c.e. sets in
d
and the corresponding degrees of their Lachlan sets. Ishmukhametov provided a systematic investigation of such degrees, and proved that for a given d.c.e. degree
d
>
0
, the class of its c.e. predecessors in which
d
is c.e., denoted as R
[d]
, can consist of either just one element, or an interval of c.e. degrees. After this, Ishmukhametov asked whether there exists a d.c.e. degree d for which the class R[d] has no minimal element. We give a positive answer to this question.</description><subject>Algebra</subject><subject>Mathematical analysis</subject><subject>Mathematical Logic and Foundations</subject><subject>Mathematical problems</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Theorems</subject><issn>0933-5846</issn><issn>1432-0665</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNp1kD9PwzAQxS0EEiHwARiQIjEb7vwvzogqKJUqdYHZslObUpqm2AkS3x5XYWBhuLvlvbt3P0KuEe4QoL5PACg5BczFBVA4IQUKzigoJU9JAQ3nVGqhzslFStusZlpjQW5W-8pWh9i7ne-qPlSLtOnGj43t_NB_XZKzYHfJX_3Okrw-Pb7MnulyNV_MHpa05agG6hpwTstaNLYBga0OXLjg1whSBM_qhrWao7ZW-FowHmQtXc7TSqfWHLjlJbmd9uYgn6NPg9n2Y9znkwaFQIZC5WdKgpOqjX1K0QdziO-djd8GwRwpmImCyRTMkUJuJWGTJ2Xt_s3HP5v_Nf0ANdtcOg</recordid><startdate>20131101</startdate><enddate>20131101</enddate><creator>Fang, Chengling</creator><creator>Wu, Guohua</creator><creator>Yamaleev, Mars</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20131101</creationdate><title>On a problem of Ishmukhametov</title><author>Fang, Chengling ; Wu, Guohua ; Yamaleev, Mars</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-b90bb85749a9041c8f34bfed1054fe2792c8318aa4e7423f575b933c5b6d303a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Algebra</topic><topic>Mathematical analysis</topic><topic>Mathematical Logic and Foundations</topic><topic>Mathematical problems</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Theorems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Fang, Chengling</creatorcontrib><creatorcontrib>Wu, Guohua</creatorcontrib><creatorcontrib>Yamaleev, Mars</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Archive for mathematical logic</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Fang, Chengling</au><au>Wu, Guohua</au><au>Yamaleev, Mars</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On a problem of Ishmukhametov</atitle><jtitle>Archive for mathematical logic</jtitle><stitle>Arch. Math. Logic</stitle><date>2013-11-01</date><risdate>2013</risdate><volume>52</volume><issue>7-8</issue><spage>733</spage><epage>741</epage><pages>733-741</pages><issn>0933-5846</issn><eissn>1432-0665</eissn><abstract>Given a d.c.e. degree
d
, consider the d.c.e. sets in
d
and the corresponding degrees of their Lachlan sets. Ishmukhametov provided a systematic investigation of such degrees, and proved that for a given d.c.e. degree
d
>
0
, the class of its c.e. predecessors in which
d
is c.e., denoted as R
[d]
, can consist of either just one element, or an interval of c.e. degrees. After this, Ishmukhametov asked whether there exists a d.c.e. degree d for which the class R[d] has no minimal element. We give a positive answer to this question.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00153-013-0340-0</doi><tpages>9</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0933-5846 |
| ispartof | Archive for mathematical logic, 2013-11, Vol.52 (7-8), p.733-741 |
| issn | 0933-5846 1432-0665 |
| language | eng |
| recordid | cdi_proquest_journals_1441214614 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Algebra Mathematical analysis Mathematical Logic and Foundations Mathematical problems Mathematics Mathematics and Statistics Theorems |
| title | On a problem of Ishmukhametov |
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