{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,9]],"date-time":"2023-04-09T23:25:16Z","timestamp":1681082716590},"reference-count":20,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2021,9,13]],"date-time":"2021-09-13T00:00:00Z","timestamp":1631491200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2021,12]]},"abstract":"Abstract<\/jats:title>It is shown that the determinacy of \n$G_{\\delta \\sigma }$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> games of length \n$\\omega ^2$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> is equivalent to the existence of a transitive model of \n${\\mathsf {KP}} + {\\mathsf {AD}} + \\Pi _1\\textrm {-MI}_{\\mathbb {R}}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> containing \n$\\mathbb {R}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. Here, \n$\\Pi _1\\textrm {-MI}_{\\mathbb {R}}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> is the axiom asserting that every monotone \n$\\Pi _1$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> operator on the real numbers has an inductive fixpoint.<\/jats:p>","DOI":"10.1017\/jsl.2021.66","type":"journal-article","created":{"date-parts":[[2021,9,13]],"date-time":"2021-09-13T08:24:13Z","timestamp":1631521453000},"page":"1676-1690","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":1,"title":["GAMES AND INDUCTION ON REALS"],"prefix":"10.1017","volume":"86","author":[{"given":"J. P.","family":"AGUILERA","sequence":"first","affiliation":[]},{"given":"P. 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D. , ${G}_{\\delta \\sigma}$ -games. Isaac Newton Institute Pre-print series No. NI12050-SAS, July 2012. 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