{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T13:23:56Z","timestamp":1648905836411},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2019,4,8]],"date-time":"2019-04-08T00:00:00Z","timestamp":1554681600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2019,9]]},"abstract":"Abstract<\/jats:title>In the topological semantics, quantified intuitionistic logic, QH, is known to be strongly complete not only for the class of all topological spaces but also for some particular topological spaces \u2014 for example, for the irrational line, ${\\Bbb P}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, and for the rational line, ${\\Bbb Q}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, in each case with a constant countable domain for the quantifiers. Each of ${\\Bbb P}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and ${\\Bbb Q}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> is a separable zero-dimensional dense-in-itself metrizable space. The main result of the current article generalizes these known results: QH is strongly complete for any zero-dimensional dense-in-itself metrizable space with a constant domain of cardinality \u2264 the space\u2019s weight; consequently, QH is strongly complete for any separable<\/jats:italic> zero-dimensional dense-in-itself metrizable space with a constant countable<\/jats:italic> domain. We also prove a result that follows from earlier work of Moerdijk: if we allow varying domains for the quantifiers, then QH is strongly complete for any dense-in-itself metrizable space with countable domains.<\/jats:p>","DOI":"10.1017\/s1755020319000170","type":"journal-article","created":{"date-parts":[[2019,4,8]],"date-time":"2019-04-08T10:51:28Z","timestamp":1554720688000},"page":"405-425","source":"Crossref","is-referenced-by-count":0,"title":["QUANTIFIED INTUITIONISTIC LOGIC OVER METRIZABLE SPACES"],"prefix":"10.1017","volume":"12","author":[{"given":"PHILIP","family":"KREMER","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2019,4,8]]},"reference":[{"key":"S1755020319000170_ref21","volume-title":"Lectures on the Curry-Howard Isomorphism","volume":"149","author":"S\u00f8rensen","year":"2006"},{"key":"S1755020319000170_ref20","volume-title":"The Mathematics of Metamathematics","author":"Rasiowa","year":"1963"},{"key":"S1755020319000170_ref19","doi-asserted-by":"publisher","DOI":"10.4064\/fm-38-1-99-126"},{"key":"S1755020319000170_ref17","volume-title":"The Stanford Encyclopedia of Philosophy","author":"Moschovakis","year":"2018"},{"key":"S1755020319000170_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/S1385-7258(82)80014-0"},{"key":"S1755020319000170_ref15","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2011.12.009"},{"key":"S1755020319000170_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2014.10.002"},{"key":"S1755020319000170_ref11","volume-title":"Quantified S4 in the Lebesgue measure algebra with a constant countable domain","author":"Kremer","year":"2014"},{"key":"S1755020319000170_ref9","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020313000087"},{"key":"S1755020319000170_ref7","volume-title":"Quantification in Nonclassical Logic","volume":"1","author":"Gabbay","year":"2009"},{"key":"S1755020319000170_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0061824"},{"key":"S1755020319000170_ref5","volume-title":"General Topology","author":"Engelking","year":"1989"},{"key":"S1755020319000170_ref4","volume-title":"Dimension Theory","author":"Engelking","year":"1978"},{"key":"S1755020319000170_ref3","volume-title":"Topology","author":"Dugundji","year":"1966"},{"key":"S1755020319000170_ref2","doi-asserted-by":"publisher","DOI":"10.1090\/mmono\/067"},{"key":"S1755020319000170_ref1","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020308080143"},{"key":"S1755020319000170_ref18","doi-asserted-by":"publisher","DOI":"10.2307\/2267135"},{"key":"S1755020319000170_ref8","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511542725"},{"key":"S1755020319000170_ref10","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020314000021"},{"key":"S1755020319000170_ref13","doi-asserted-by":"publisher","DOI":"10.2307\/2267105"},{"key":"S1755020319000170_ref14","doi-asserted-by":"publisher","DOI":"10.2307\/1969080"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020319000170","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,29]],"date-time":"2019-08-29T09:05:53Z","timestamp":1567069553000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020319000170\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,8]]},"references-count":21,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,9]]}},"alternative-id":["S1755020319000170"],"URL":"https:\/\/doi.org\/10.1017\/s1755020319000170","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,4,8]]}}}