{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,21]],"date-time":"2023-09-21T05:13:40Z","timestamp":1695273220996},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"7-8","license":[{"start":{"date-parts":[[2023,5,18]],"date-time":"2023-05-18T00:00:00Z","timestamp":1684368000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,5,18]],"date-time":"2023-05-18T00:00:00Z","timestamp":1684368000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Albert-Ludwigs-Universit\u00e4t Freiburg im Breisgau"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Arch. Math. Logic"],"published-print":{"date-parts":[[2023,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We define and investigate versions of Silver and Mathias forcing with respect to lower and upper density. We focus on properness, Axiom A, chain conditions, preservation of cardinals and adding Cohen reals. We find rough forcings that collapse <jats:inline-formula><jats:alternatives><jats:tex-math>$$2^\\omega $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mn>2<\/mml:mn>\n                    <mml:mi>\u03c9<\/mml:mi>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> to <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\omega $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03c9<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, while others are surprisingly gentle. We also study connections between regularity properties induced by these parametrized forcing notions and the Baire property.\n<\/jats:p>","DOI":"10.1007\/s00153-023-00881-7","type":"journal-article","created":{"date-parts":[[2023,5,18]],"date-time":"2023-05-18T11:03:03Z","timestamp":1684407783000},"page":"965-990","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Mathias and silver forcing parametrized by density"],"prefix":"10.1007","volume":"62","author":[{"given":"Giorgio","family":"Laguzzi","sequence":"first","affiliation":[]},{"given":"Heike","family":"Mildenberger","sequence":"additional","affiliation":[]},{"given":"Brendan","family":"Stuber-Rousselle","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,5,18]]},"reference":[{"key":"881_CR1","unstructured":"Bartoszy\u0144ski, Tomek, Judah, Haim: Set Theory, on the Structure of the Real Line. 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