Baire spaces and infinite games
It is well known that if the nonempty player of the Banach–Mazur game has a winning strategy on a space, then that space is Baire in all powers even in the box product topology. The converse of this implication may also be true: We know of no consistency result to the contrary. In this paper we esta...
Gespeichert in:
| Veröffentlicht in: | Archive for mathematical logic 2016-02, Vol.55 (1-2), p.85-104 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 104 |
|---|---|
| container_issue | 1-2 |
| container_start_page | 85 |
| container_title | Archive for mathematical logic |
| container_volume | 55 |
| creator | Galvin, Fred Scheepers, Marion |
| description | It is well known that if the nonempty player of the Banach–Mazur game has a winning strategy on a space, then that space is Baire in all powers even in the box product topology. The converse of this implication may also be true: We know of no consistency result to the contrary. In this paper we establish the consistency of the converse relative to the consistency of the existence of a proper class of measurable cardinals. |
| doi_str_mv | 10.1007/s00153-015-0461-8 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1835579234</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1835579234</sourcerecordid><originalsourceid>FETCH-LOGICAL-c419t-a628756222fba914c183960ba9773f2ba8d32aaf7e76f6c5b7b3e95aebb9c8663</originalsourceid><addsrcrecordid>eNp1kEtLAzEUhYMoWKs_wJUDbtxEk5v3UosvKLjRdcikSZnSztTcduG_N2UEQXBzzl1853A5hFxydssZM3fIGFeCVqFMak7tEZlwKYAyrdUxmTAnBFVW6lNyhriqNFjLJ-TqIXQlNbgNMWET-kXT9bnru11qlmGT8Jyc5LDGdPHjU_Lx9Pg-e6Hzt-fX2f2cRsndjgYN1igNALkNjsvIrXCa1dsYkaENdiEghGyS0VlH1ZpWJKdCalsXrdZiSm7G3m0ZPvcJd37TYUzrdejTsEdf-5QyDoSs6PUfdDXsS1-_88C0NCBBmErxkYplQCwp-23pNqF8ec78YTI_Tuar-MNk3tYMjBmsbL9M5bf5_9A3ALprhA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2064724237</pqid></control><display><type>article</type><title>Baire spaces and infinite games</title><source>SpringerNature Journals</source><creator>Galvin, Fred ; Scheepers, Marion</creator><creatorcontrib>Galvin, Fred ; Scheepers, Marion</creatorcontrib><description>It is well known that if the nonempty player of the Banach–Mazur game has a winning strategy on a space, then that space is Baire in all powers even in the box product topology. The converse of this implication may also be true: We know of no consistency result to the contrary. In this paper we establish the consistency of the converse relative to the consistency of the existence of a proper class of measurable cardinals.</description><identifier>ISSN: 0933-5846</identifier><identifier>EISSN: 1432-0665</identifier><identifier>DOI: 10.1007/s00153-015-0461-8</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Algebra ; Archives ; Consistency ; Game theory ; Games ; Mathematical logic ; Mathematical Logic and Foundations ; Mathematics ; Mathematics and Statistics ; Players ; Strategy ; Topology</subject><ispartof>Archive for mathematical logic, 2016-02, Vol.55 (1-2), p.85-104</ispartof><rights>Springer-Verlag Berlin Heidelberg 2015</rights><rights>Copyright Springer Science & Business Media 2016</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c419t-a628756222fba914c183960ba9773f2ba8d32aaf7e76f6c5b7b3e95aebb9c8663</citedby><cites>FETCH-LOGICAL-c419t-a628756222fba914c183960ba9773f2ba8d32aaf7e76f6c5b7b3e95aebb9c8663</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/s00153-015-0461-8$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00153-015-0461-8$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Galvin, Fred</creatorcontrib><creatorcontrib>Scheepers, Marion</creatorcontrib><title>Baire spaces and infinite games</title><title>Archive for mathematical logic</title><addtitle>Arch. Math. Logic</addtitle><description>It is well known that if the nonempty player of the Banach–Mazur game has a winning strategy on a space, then that space is Baire in all powers even in the box product topology. The converse of this implication may also be true: We know of no consistency result to the contrary. In this paper we establish the consistency of the converse relative to the consistency of the existence of a proper class of measurable cardinals.</description><subject>Algebra</subject><subject>Archives</subject><subject>Consistency</subject><subject>Game theory</subject><subject>Games</subject><subject>Mathematical logic</subject><subject>Mathematical Logic and Foundations</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Players</subject><subject>Strategy</subject><subject>Topology</subject><issn>0933-5846</issn><issn>1432-0665</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp1kEtLAzEUhYMoWKs_wJUDbtxEk5v3UosvKLjRdcikSZnSztTcduG_N2UEQXBzzl1853A5hFxydssZM3fIGFeCVqFMak7tEZlwKYAyrdUxmTAnBFVW6lNyhriqNFjLJ-TqIXQlNbgNMWET-kXT9bnru11qlmGT8Jyc5LDGdPHjU_Lx9Pg-e6Hzt-fX2f2cRsndjgYN1igNALkNjsvIrXCa1dsYkaENdiEghGyS0VlH1ZpWJKdCalsXrdZiSm7G3m0ZPvcJd37TYUzrdejTsEdf-5QyDoSs6PUfdDXsS1-_88C0NCBBmErxkYplQCwp-23pNqF8ec78YTI_Tuar-MNk3tYMjBmsbL9M5bf5_9A3ALprhA</recordid><startdate>20160201</startdate><enddate>20160201</enddate><creator>Galvin, Fred</creator><creator>Scheepers, Marion</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>20160201</creationdate><title>Baire spaces and infinite games</title><author>Galvin, Fred ; Scheepers, Marion</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c419t-a628756222fba914c183960ba9773f2ba8d32aaf7e76f6c5b7b3e95aebb9c8663</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Algebra</topic><topic>Archives</topic><topic>Consistency</topic><topic>Game theory</topic><topic>Games</topic><topic>Mathematical logic</topic><topic>Mathematical Logic and Foundations</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Players</topic><topic>Strategy</topic><topic>Topology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Galvin, Fred</creatorcontrib><creatorcontrib>Scheepers, Marion</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>Galvin, Fred</au><au>Scheepers, Marion</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Baire spaces and infinite games</atitle><jtitle>Archive for mathematical logic</jtitle><stitle>Arch. Math. Logic</stitle><date>2016-02-01</date><risdate>2016</risdate><volume>55</volume><issue>1-2</issue><spage>85</spage><epage>104</epage><pages>85-104</pages><issn>0933-5846</issn><eissn>1432-0665</eissn><abstract>It is well known that if the nonempty player of the Banach–Mazur game has a winning strategy on a space, then that space is Baire in all powers even in the box product topology. The converse of this implication may also be true: We know of no consistency result to the contrary. In this paper we establish the consistency of the converse relative to the consistency of the existence of a proper class of measurable cardinals.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00153-015-0461-8</doi><tpages>20</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0933-5846 |
| ispartof | Archive for mathematical logic, 2016-02, Vol.55 (1-2), p.85-104 |
| issn | 0933-5846 1432-0665 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1835579234 |
| source | SpringerNature Journals |
| subjects | Algebra Archives Consistency Game theory Games Mathematical logic Mathematical Logic and Foundations Mathematics Mathematics and Statistics Players Strategy Topology |
| title | Baire spaces and infinite games |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-04T06%3A25%3A11IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Baire%20spaces%20and%20infinite%20games&rft.jtitle=Archive%20for%20mathematical%20logic&rft.au=Galvin,%20Fred&rft.date=2016-02-01&rft.volume=55&rft.issue=1-2&rft.spage=85&rft.epage=104&rft.pages=85-104&rft.issn=0933-5846&rft.eissn=1432-0665&rft_id=info:doi/10.1007/s00153-015-0461-8&rft_dat=%3Cproquest_cross%3E1835579234%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2064724237&rft_id=info:pmid/&rfr_iscdi=true |