A note on the eightfold way
Assuming the existence of a Mahlo cardinal, we construct a model in which there exists an \omega _2-Aronszajn tree, the \omega _1-approachability property fails, and every stationary subset of \omega _2 \cap \text {cof}(\omega ) reflects. This solves an open problem of Cummings et al. [J. Symb. Log....
Gespeichert in:
| Veröffentlicht in: | Proceedings of the American Mathematical Society 2020-03, Vol.148 (3), p.1283-1293 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1293 |
|---|---|
| container_issue | 3 |
| container_start_page | 1283 |
| container_title | Proceedings of the American Mathematical Society |
| container_volume | 148 |
| creator | Gilton, Thomas Krueger, John |
| description | Assuming the existence of a Mahlo cardinal, we construct a model in which there exists an \omega _2-Aronszajn tree, the \omega _1-approachability property fails, and every stationary subset of \omega _2 \cap \text {cof}(\omega ) reflects. This solves an open problem of Cummings et al. [J. Symb. Log. 83 (2018), no. 1, pp. 349-371] |
| doi_str_mv | 10.1090/proc/14771 |
| format | Article |
| fullrecord | <record><control><sourceid>ams_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1090_proc_14771</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_1090_proc_14771</sourcerecordid><originalsourceid>FETCH-LOGICAL-a261t-bd67c3c7a5c6e16988e53a925cc01a2e15853d3a6498f49b5042479639b5d4bb3</originalsourceid><addsrcrecordid>eNp9j01LAzEURYMoOFY3bt1k40aIzcv3W5ZiVSi40XXIZDK20jYlGZD-e6fWtat7LxwuHEJugT8CRz7dlxynoKyFM9IAd44ZJ8w5aTjngiFKvCRXtX6NE1DZhtzN6C4PieYdHVaJpvXnaujzpqPf4XBNLvqwqenmLyfkY_H0Pn9hy7fn1_lsyYIwMLC2MzbKaIOOJoFB55KWAYWOkUMQCbTTspPBKHS9wlZzJZRFI8faqbaVE_Jw-o0l11pS7_dlvQ3l4IH7o5Y_avlfrRG-P8FhW__jfgB6NUoz</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>A note on the eightfold way</title><source>American Mathematical Society Journals</source><creator>Gilton, Thomas ; Krueger, John</creator><creatorcontrib>Gilton, Thomas ; Krueger, John</creatorcontrib><description>Assuming the existence of a Mahlo cardinal, we construct a model in which there exists an \omega _2-Aronszajn tree, the \omega _1-approachability property fails, and every stationary subset of \omega _2 \cap \text {cof}(\omega ) reflects. This solves an open problem of Cummings et al. [J. Symb. Log. 83 (2018), no. 1, pp. 349-371]</description><identifier>ISSN: 0002-9939</identifier><identifier>EISSN: 1088-6826</identifier><identifier>DOI: 10.1090/proc/14771</identifier><language>eng</language><ispartof>Proceedings of the American Mathematical Society, 2020-03, Vol.148 (3), p.1283-1293</ispartof><rights>Copyright 2019, American Mathematical Society</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-a261t-bd67c3c7a5c6e16988e53a925cc01a2e15853d3a6498f49b5042479639b5d4bb3</citedby><cites>FETCH-LOGICAL-a261t-bd67c3c7a5c6e16988e53a925cc01a2e15853d3a6498f49b5042479639b5d4bb3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttp://www.ams.org/proc/2020-148-03/S0002-9939-2019-14771-7/S0002-9939-2019-14771-7.pdf$$EPDF$$P50$$Gams$$H</linktopdf><linktohtml>$$Uhttp://www.ams.org/proc/2020-148-03/S0002-9939-2019-14771-7/$$EHTML$$P50$$Gams$$H</linktohtml><link.rule.ids>68,314,780,784,23328,27924,27925,77836,77846</link.rule.ids></links><search><creatorcontrib>Gilton, Thomas</creatorcontrib><creatorcontrib>Krueger, John</creatorcontrib><title>A note on the eightfold way</title><title>Proceedings of the American Mathematical Society</title><description>Assuming the existence of a Mahlo cardinal, we construct a model in which there exists an \omega _2-Aronszajn tree, the \omega _1-approachability property fails, and every stationary subset of \omega _2 \cap \text {cof}(\omega ) reflects. This solves an open problem of Cummings et al. [J. Symb. Log. 83 (2018), no. 1, pp. 349-371]</description><issn>0002-9939</issn><issn>1088-6826</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9j01LAzEURYMoOFY3bt1k40aIzcv3W5ZiVSi40XXIZDK20jYlGZD-e6fWtat7LxwuHEJugT8CRz7dlxynoKyFM9IAd44ZJ8w5aTjngiFKvCRXtX6NE1DZhtzN6C4PieYdHVaJpvXnaujzpqPf4XBNLvqwqenmLyfkY_H0Pn9hy7fn1_lsyYIwMLC2MzbKaIOOJoFB55KWAYWOkUMQCbTTspPBKHS9wlZzJZRFI8faqbaVE_Jw-o0l11pS7_dlvQ3l4IH7o5Y_avlfrRG-P8FhW__jfgB6NUoz</recordid><startdate>20200301</startdate><enddate>20200301</enddate><creator>Gilton, Thomas</creator><creator>Krueger, John</creator><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20200301</creationdate><title>A note on the eightfold way</title><author>Gilton, Thomas ; Krueger, John</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a261t-bd67c3c7a5c6e16988e53a925cc01a2e15853d3a6498f49b5042479639b5d4bb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gilton, Thomas</creatorcontrib><creatorcontrib>Krueger, John</creatorcontrib><collection>CrossRef</collection><jtitle>Proceedings of the American Mathematical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gilton, Thomas</au><au>Krueger, John</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A note on the eightfold way</atitle><jtitle>Proceedings of the American Mathematical Society</jtitle><date>2020-03-01</date><risdate>2020</risdate><volume>148</volume><issue>3</issue><spage>1283</spage><epage>1293</epage><pages>1283-1293</pages><issn>0002-9939</issn><eissn>1088-6826</eissn><abstract>Assuming the existence of a Mahlo cardinal, we construct a model in which there exists an \omega _2-Aronszajn tree, the \omega _1-approachability property fails, and every stationary subset of \omega _2 \cap \text {cof}(\omega ) reflects. This solves an open problem of Cummings et al. [J. Symb. Log. 83 (2018), no. 1, pp. 349-371]</abstract><doi>10.1090/proc/14771</doi><tpages>11</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0002-9939 |
| ispartof | Proceedings of the American Mathematical Society, 2020-03, Vol.148 (3), p.1283-1293 |
| issn | 0002-9939 1088-6826 |
| language | eng |
| recordid | cdi_crossref_primary_10_1090_proc_14771 |
| source | American Mathematical Society Journals |
| title | A note on the eightfold way |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-28T09%3A38%3A06IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-ams_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20note%20on%20the%20eightfold%20way&rft.jtitle=Proceedings%20of%20the%20American%20Mathematical%20Society&rft.au=Gilton,%20Thomas&rft.date=2020-03-01&rft.volume=148&rft.issue=3&rft.spage=1283&rft.epage=1293&rft.pages=1283-1293&rft.issn=0002-9939&rft.eissn=1088-6826&rft_id=info:doi/10.1090/proc/14771&rft_dat=%3Cams_cross%3E10_1090_proc_14771%3C/ams_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |