{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:09:19Z","timestamp":1753884559351,"version":"3.41.2"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"name":"NSF","award":["DMS-1600263"],"award-info":[{"award-number":["DMS-1600263"]}]},{"name":"NSF","award":["DMS-1854107"],"award-info":[{"award-number":["DMS-1854107"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2023,8]]},"abstract":"<jats:p> We characterize the completely determined Borel subsets of HYP as exactly the [Formula: see text] subsets of HYP. As a result, HYP believes there is a Borel well-ordering of the reals, that the Borel Dual Ramsey Theorem fails, and that every Borel d-regular bipartite graph has a Borel perfect matching, among other examples. Therefore, the Borel Dual Ramsey Theorem and several theorems of descriptive combinatorics are not theories of hyperarithmetic analysis. In the case of the Borel Dual Ramsey Theorem, this answers a question of Astor, Dzhafarov, Montalb\u00e1n, Solomon and the third author. <\/jats:p>","DOI":"10.1142\/s0219061322500234","type":"journal-article","created":{"date-parts":[[2022,6,17]],"date-time":"2022-06-17T09:18:28Z","timestamp":1655457508000},"source":"Crossref","is-referenced-by-count":0,"title":["Borel combinatorics fail in <i>HYP<\/i>"],"prefix":"10.1142","volume":"23","author":[{"given":"Henry","family":"Towsner","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104-6395, USA"}]},{"given":"Rose","family":"Weisshaar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Wake Forest University, 127 Manchester Hall, Winston-Salem, NC 27109, USA"}]},{"given":"Linda","family":"Westrick","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Penn State University, University Park, PA 16802, USA"}]}],"member":"219","published-online":{"date-parts":[[2022,12,17]]},"reference":[{"issue":"1","key":"S0219061322500234BIB001","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1017\/jsl.2019.64","volume":"85","author":"Astor E. 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