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Log."],"published-print":{"date-parts":[[2023,8]]},"abstract":"<jats:p>We investigate the interaction between compactness principles and guessing principles in the Radin forcing extensions. In particular, we show that in any Radin forcing extension with respect to a measure sequence on [Formula: see text], if [Formula: see text] is weakly compact, then [Formula: see text] holds. This provides contrast with a well-known theorem of Woodin, who showed that in a certain Radin extension over a suitably prepared ground model relative to the existence of large cardinals, the diamond principle fails at a strongly inaccessible Mahlo cardinal. Refining the analysis of the Radin extensions, we consistently demonstrate a scenario where a compactness principle, stronger than the diagonal stationary reflection principle, holds yet the diamond principle fails at a strongly inaccessible cardinal, improving a result from [O. B. -Neria, Diamonds, compactness, and measure sequences, J. Math. Log. 19(1) (2019) 1950002].<\/jats:p>","DOI":"10.1142\/s0219061322500246","type":"journal-article","created":{"date-parts":[[2022,6,17]],"date-time":"2022-06-17T09:18:28Z","timestamp":1655457508000},"source":"Crossref","is-referenced-by-count":2,"title":["Compactness and guessing principles in the Radin extensions"],"prefix":"10.1142","volume":"23","author":[{"given":"Omer","family":"Ben-Neria","sequence":"first","affiliation":[{"name":"Einstein Institute of Mathematics, The Hebrew University, Givan Ram, Jerusalem, Israel"}]},{"given":"Jing","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Room 6290, University of Toronto, 40 St George St, Toronto, ON M5S 2E4, Canada"}]}],"member":"219","published-online":{"date-parts":[[2022,12,17]]},"reference":[{"issue":"1","key":"S0219061322500246BIB001","doi-asserted-by":"crossref","first-page":"1950002","DOI":"10.1142\/S0219061319500028","volume":"19","author":"Ben-Neria O.","year":"2019","journal-title":"J. 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