{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T08:49:23Z","timestamp":1649062163854},"reference-count":23,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2013,4,8]],"date-time":"2013-04-08T00:00:00Z","timestamp":1365379200000},"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":[[2013,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We study the model-theoretic aspects of a probability logic suited for talking about measure spaces. This nonclassical logic has a model theory rather different from that of classical predicate logic. In general, not every satisfiable set of sentences has a countable model, but we show that one can always build a model on the unit interval. Also, the probability logic under consideration is not compact. However, using ultraproducts we can prove a compactness theorem for a certain class of weak models.<\/jats:p>","DOI":"10.1017\/s1755020313000063","type":"journal-article","created":{"date-parts":[[2013,4,8]],"date-time":"2013-04-08T09:53:53Z","timestamp":1365414833000},"page":"367-393","source":"Crossref","is-referenced-by-count":4,"title":["MODEL THEORY OF MEASURE SPACES AND PROBABILITY LOGIC"],"prefix":"10.1017","volume":"6","author":[{"given":"RUTGER","family":"KUYPER","sequence":"first","affiliation":[]},{"given":"SEBASTIAAN A.","family":"TERWIJN","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2013,4,8]]},"reference":[{"key":"S1755020313000063_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-34514-5"},{"key":"S1755020313000063_ref8","first-page":"1375","volume-title":"Proceedings of 11th International Joint Conference on Artificial Intelligence (IJCAI-89)","author":"Halpern","year":"1989"},{"key":"S1755020313000063_ref5","doi-asserted-by":"publisher","DOI":"10.1086\/286851"},{"key":"S1755020313000063_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-009-0133-7"},{"key":"S1755020313000063_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jal.2007.11.003"},{"key":"S1755020313000063_ref6","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511896972"},{"key":"S1755020313000063_ref12","doi-asserted-by":"publisher","DOI":"10.1007\/s11229-004-6153-2"},{"key":"S1755020313000063_ref22","doi-asserted-by":"publisher","DOI":"10.1016\/S0004-3702(00)00002-3"},{"key":"S1755020313000063_ref20","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/exi032"},{"key":"S1755020313000063_ref13","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/3897.001.0001","volume-title":"An Introduction to Computational Learning Theory","author":"Kearns","year":"1994"},{"key":"S1755020313000063_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/BF02759729"},{"key":"S1755020313000063_ref1","volume-title":"Infinite-dimensional Analysis: A Hitchhiker\u2019s Guide","author":"Aliprantis","year":"2006"},{"key":"S1755020313000063_ref10","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511551574"},{"key":"S1755020313000063_ref15","first-page":"509","volume-title":"Model-Theoretic Logics","author":"Keisler","year":"1985"},{"key":"S1755020313000063_ref19","first-page":"579","volume-title":"Model Theoretic Logics","author":"Steinhorn","year":"1985"},{"key":"S1755020313000063_ref17","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1975-0390154-8"},{"key":"S1755020313000063_ref21","first-page":"441","volume-title":"Proceedings of Logical Foundations of Computer Science","author":"Terwijn","year":"2009"},{"key":"S1755020313000063_ref23","doi-asserted-by":"publisher","DOI":"10.1007\/s11229-008-9357-z"},{"key":"S1755020313000063_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01211866"},{"key":"S1755020313000063_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4190-4"},{"key":"S1755020313000063_ref16","volume-title":"Set Theory: An Introduction to Independence Proofs","author":"Kunen","year":"1983"},{"key":"S1755020313000063_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71672-0"},{"key":"S1755020313000063_ref3","volume-title":"Lattice Theory (revised edition).","author":"Birkhoff","year":"1948"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020313000063","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,23]],"date-time":"2019-04-23T20:06:31Z","timestamp":1556049991000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020313000063\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,4,8]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2013,9]]}},"alternative-id":["S1755020313000063"],"URL":"https:\/\/doi.org\/10.1017\/s1755020313000063","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,4,8]]}}}