{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T13:59:19Z","timestamp":1697637559435},"reference-count":7,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":3603,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1997,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>An interesting positive theory is the GPK theory. The models of this theory include all hyperuniverses (see [5] for a definition of these ones). Here we add a form of the axiom of infinity and a new scheme to obtain GPK<jats:sub>\u221e<\/jats:sub><jats:sup>+<\/jats:sup>. We show that in these conditions, we can interprete the Kelley\u2010Morse theory (KM) in GPK<jats:sub>\u221e<\/jats:sub><jats:sup>+<\/jats:sup> (Theorem 3.7). This needs a preliminary property which give an interpretation of the Zermelo\u2010Fraenkel set theory (ZF) in GPK<jats:sub>\u221e<\/jats:sub><jats:sup>+<\/jats:sup>. We also see what happens in the original GPK theory. Before doing this, we first need to study the basic properties of the theory. This is done in the first two sections.<\/jats:p>","DOI":"10.1002\/malq.19970430309","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T16:20:41Z","timestamp":1180455641000},"page":"369-377","source":"Crossref","is-referenced-by-count":5,"title":["An Interpretation of the Zermelo\u2010Fraenkel Set Theory and the Kelley\u2010Morse Set Theory in a Positive Theory"],"prefix":"10.1002","volume":"43","author":[{"given":"Olivier","family":"Esser","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","volume-title":"Set Theory and the Continuum Hypothesis","author":"Cohen P. J.","year":"1966"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19960420109"},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","first-page":"1401","DOI":"10.2307\/2274822","article-title":"The consistency problem for positive comprehension principles","volume":"54","author":"Forti M.","year":"1989","journal-title":"J. Symbolic Logic"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-9828-2_21"},{"key":"e_1_2_1_6_2","unstructured":"Forti M.andF.Honsell A general construction of hyperuniverses. Quaderni dell'Istituto di Matematiche Applicate \u201cU. Dini\u201d Facolt\u00e0 di Ingegnria Universit\u00e1 di Pisa 1992."},{"key":"e_1_2_1_7_2","volume-title":"Th\u00e9orie axiomatique des ensembles","author":"Krivine J.\u2010L.","year":"1969"},{"key":"e_1_2_1_8_2","unstructured":"Weydert E. How to approximate the naive comprehension scheme inside of classical logic. Ph. D. thesis Bonner Mathematische Schriften 194 Bonn1989."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19970430309","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19970430309","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,10]],"date-time":"2023-10-10T05:38:20Z","timestamp":1696916300000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19970430309"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,1]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1997,1]]}},"alternative-id":["10.1002\/malq.19970430309"],"URL":"https:\/\/doi.org\/10.1002\/malq.19970430309","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,1]]}}}