{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T08:43:00Z","timestamp":1695890580060},"reference-count":8,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":5430,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1992,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper we investigate Boolean algebras and their subalgebras in Alternative Set Theory (AST). We show that any two countable atomless Boolean algebras are isomorphic and we give an example of such a Boolean algebra. One other main result is, that there is an infinite Boolean algebra freely generated by a set. At the end of the paper we show that the sentence \u201cThere is no non\u2010trivial free group which is a set\u201d is consistent with AST.<\/jats:p>","DOI":"10.1002\/malq.19920380135","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T05:50:11Z","timestamp":1180417811000},"page":"373-382","source":"Crossref","is-referenced-by-count":0,"title":["BOOLEAN ALGEBRAS IN AST"],"prefix":"10.1002","volume":"38","author":[{"given":"Klaus","family":"Schumacher","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"Felgner U. Mathematische Logik I. Vorlesungsskript WS 1988\/89 Universit\u00e4t T\u00fcbingen."},{"key":"e_1_2_1_3_2","volume-title":"Boolesche Algebra","author":"Gumm H. P.","year":"1981"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02308-2"},{"key":"e_1_2_1_5_2","volume-title":"Algebra","author":"Meyberg K.","year":"1975"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9452-5"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0096906"},{"key":"e_1_2_1_8_2","first-page":"697","article-title":"Metamathematics of the alternative set theory I","volume":"20","author":"Sochor A.","year":"1979","journal-title":"Commentationes Mathematicae Universitatis Carolinae"},{"key":"e_1_2_1_9_2","volume-title":"Mathematics in the Alternative Set Theory","author":"Vop\u00eanka P.","year":"1979"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19920380135","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19920380135","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T20:34:31Z","timestamp":1695846871000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19920380135"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,1]]},"references-count":8,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1992,1]]}},"alternative-id":["10.1002\/malq.19920380135"],"URL":"https:\/\/doi.org\/10.1002\/malq.19920380135","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,1]]}}}