{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T22:04:25Z","timestamp":1747173865033,"version":"3.40.5"},"reference-count":26,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2021,9,27]],"date-time":"2021-09-27T00:00:00Z","timestamp":1632700800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2023,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The purpose of this paper is to compare the notion of a <jats:italic>Grzegorczyk point<\/jats:italic> introduced in [19] (and thoroughly investigated in [3, 14, 16, 18]) to the standard notions of a <jats:italic>filter<\/jats:italic> in Boolean algebras and <jats:italic>round filter<\/jats:italic> in Boolean contact algebras. In particular, we compare Grzegorczyk points to filters and ultrafilters of atomic and atomless algebras. We also prove how a certain extra axiom influences topological spaces for Grzegorczyk contact algebras. Last but not least, we do not refrain from a philosophical interpretation of the results from the paper.<\/jats:p>","DOI":"10.1017\/s1755020321000459","type":"journal-article","created":{"date-parts":[[2021,9,27]],"date-time":"2021-09-27T14:19:22Z","timestamp":1632752362000},"page":"509-528","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":2,"title":["GRZEGORCZYK POINTS AND FILTERS IN BOOLEAN CONTACT ALGEBRAS"],"prefix":"10.1017","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3379-0577","authenticated-orcid":false,"given":"RAFA\u0141","family":"GRUSZCZY\u0143SKI","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9133-5081","authenticated-orcid":false,"given":"ANDRZEJ","family":"PIETRUSZCZAK","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2021,9,27]]},"reference":[{"key":"S1755020321000459_r1","first-page":"1235","volume-title":"Handbook on Boolean Algebras","volume":"3","author":"Balcar","year":"1989"},{"key":"S1755020321000459_r2","first-page":"1239","volume-title":"Handbook on Boolean Algebras","volume":"3","author":"Balcar","year":"1989"},{"key":"S1755020321000459_r3","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1039886519"},{"key":"S1755020321000459_r5","doi-asserted-by":"publisher","DOI":"10.1023\/A:1009712514511"},{"key":"S1755020321000459_r15","doi-asserted-by":"publisher","DOI":"10.12775\/LLP.2009.009"},{"key":"S1755020321000459_r12","doi-asserted-by":"publisher","DOI":"10.1007\/11734673_6"},{"key":"S1755020321000459_r19","doi-asserted-by":"publisher","DOI":"10.1007\/BF00485101"},{"key":"S1755020321000459_r21","unstructured":"[21] Hamkins, J. , & Seabold, D. (2012). Well-founded Boolean ultrapowers as large cardinal embeddings. 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Published by Cambridge University Press on behalf of The Association for Symbolic Logic","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}