{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T21:58:31Z","timestamp":1649195911786},"reference-count":9,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":12703,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1979,6]]},"abstract":"<jats:p>Consistency properties and their model existence theorems have provided an important method of constructing models for fragments of <jats:italic>L<\/jats:italic><jats:sub>\u221e\u03c9<\/jats:sub>. In [E] Ellentuck extended this construction to Suslin logic. One of his extensions, the Borel consistency property, has its extra rule based not on the semantic interpretation of the extra symbols but rather on a theorem of Sierpinski about the classical operation <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S002248120004888X_inline1\" \/>. In this paper we extend that consistency property to the game logic <jats:italic>L<jats:sub>G<\/jats:sub><\/jats:italic> and use it to show how one can extend results about <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S002248120004888X_inline2\" \/> and its countable fragments to <jats:italic>L<jats:sub>G<\/jats:sub><\/jats:italic> and certain of its countable fragments. The particular formation of <jats:italic>L<jats:sub>G<\/jats:sub><\/jats:italic> which we use will allow in the game quantifier infinite alternation of countable conjunctions and disjunctions as well as infinite alternation of quantifiers. In this way <jats:italic>L<jats:sub>G<\/jats:sub><\/jats:italic> can be viewed as an extension of Suslin logic.<\/jats:p>","DOI":"10.2307\/2273724","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:50:09Z","timestamp":1146952209000},"page":"147-152","source":"Crossref","is-referenced-by-count":0,"title":["Some model theory for game logics"],"prefix":"10.1017","volume":"44","author":[{"given":"Judy","family":"Green","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120004888X_ref004","volume-title":"Model theory for infinitary logic","author":"Keisler","year":"1971"},{"key":"S002248120004888X_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0066791"},{"key":"S002248120004888X_ref009","doi-asserted-by":"publisher","DOI":"10.4064\/fm-82-3-269-294"},{"key":"S002248120004888X_ref002","first-page":"568","volume":"43","author":"Burgess","year":"1978","journal-title":"On the Hanf number of Souslin logic"},{"key":"S002248120004888X_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0079692"},{"key":"S002248120004888X_ref005","volume-title":"Topology, vol. I","author":"Kurotowski","year":"1966"},{"key":"S002248120004888X_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(72)90002-2"},{"key":"S002248120004888X_ref003","first-page":"567","volume":"40","author":"Ellentuck","year":"1975","journal-title":"The foundations of Suslin logic"},{"key":"S002248120004888X_ref006","volume-title":"Elementary induction on abstract structures","author":"Moschovakis","year":"1974"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120004888X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,26]],"date-time":"2019-05-26T21:20:50Z","timestamp":1558905650000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120004888X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1979,6]]},"references-count":9,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1979,6]]}},"alternative-id":["S002248120004888X"],"URL":"https:\/\/doi.org\/10.2307\/2273724","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1979,6]]}}}