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We also show some barriers to getting the tree property and a saturated ideal simultaneously on a successor cardinal from conventional forcing methods. <\/jats:p>","DOI":"10.1142\/s0219061322500167","type":"journal-article","created":{"date-parts":[[2022,6,17]],"date-time":"2022-06-17T09:18:28Z","timestamp":1655457508000},"source":"Crossref","is-referenced-by-count":1,"title":["Compactness versus hugeness at successor cardinals"],"prefix":"10.1142","volume":"23","author":[{"given":"Sean","family":"Cox","sequence":"first","affiliation":[{"name":"Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, 1015 Floyd Avenue, Richmond, Virginia 23284, USA"}]},{"given":"Monroe","family":"Eskew","sequence":"additional","affiliation":[{"name":"Universit\u00e4t Wien Institut f\u00fcr Mathematik Kurt, G\u00f6del Research Center Kolingasse 14-16 1090 Wien, Austria"}]}],"member":"219","published-online":{"date-parts":[[2022,9,27]]},"reference":[{"key":"S0219061322500167BIB001","doi-asserted-by":"crossref","first-page":"913","DOI":"10.1016\/B978-0-444-86580-9.50024-0","volume-title":"Handbook of Set-Theoretic Topology","author":"Baumgartner J. 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