乐胖代购免代理版

{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,2]],"date-time":"2024-08-02T14:36:13Z","timestamp":1722609373031},"reference-count":23,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2020,10,30]],"date-time":"2020-10-30T00:00:00Z","timestamp":1604016000000},"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":[[2021,6]]},"abstract":"Abstract<\/jats:title>In contrast to the robust mutual interpretability phenomenon in set theory, Ali Enayat proved that bi-interpretation is absent: distinct theories extending ZF are never bi-interpretable and models of ZF are bi-interpretable only when they are isomorphic. Nevertheless, for natural weaker set theories, we prove, including Zermelo\u2013Fraenkel set theory

\n$\\mathrm {ZFC}^{-}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> without power set and Zermelo set theory Z, there are nontrivial instances of bi-interpretation. Specifically, there are well-founded models of

\n$\\mathrm {ZFC}^{-}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> that are bi-interpretable, but not isomorphic\u2014even

\n$\\langle H_{\\omega _1},\\in \\rangle $\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and

\n$ \\langle H_{\\omega _2},\\in \\rangle $\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> can be bi-interpretable\u2014and there are distinct bi-interpretable theories extending

\n$\\mathrm {ZFC}^{-}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. Similarly, using a construction of Mathias, we prove that every model of ZF is bi-interpretable with a model of Zermelo set theory in which the replacement axiom fails.<\/jats:p>","DOI":"10.1017\/jsl.2020.72","type":"journal-article","created":{"date-parts":[[2020,10,30]],"date-time":"2020-10-30T01:59:25Z","timestamp":1604023165000},"page":"609-634","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":4,"title":["BI-INTERPRETATION IN WEAK SET THEORIES"],"prefix":"10.1017","volume":"86","author":[{"given":"ALFREDO","family":"ROQUE FREIRE","sequence":"first","affiliation":[]},{"given":"JOEL DAVID","family":"HAMKINS","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2020,10,30]]},"reference":[{"key":"S0022481220000729_r19","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2007.07.002"},{"key":"S0022481220000729_r13","unstructured":"[13] Hamkins, J. D. , Different set theories are never bi-interpretable. Mathematics and Philosophy of the Infinite, 2018. Available at http:\/\/jdh.hamkins.org\/different-set-theories-are-never-bi-interpretable\/ (accessed 27 March, 2018)."},{"key":"S0022481220000729_r6","doi-asserted-by":"publisher","DOI":"10.1590\/0100-6045.2019.v42n2.rf"},{"key":"S0022481220000729_r4","volume-title":"The Logica Yearbook 2007","author":"Freire","year":"2008"},{"key":"S0022481220000729_r12","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020311000359"},{"key":"S0022481220000729_r2","doi-asserted-by":"publisher","DOI":"10.1016\/S1385-7258(65)50063-9"},{"key":"S0022481220000729_r20","first-page":"487","article-title":"Slim models of Zermelo set theory","volume":"66","author":"Mathias","year":"2001","journal-title":"Journal,"},{"key":"S0022481220000729_r8","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2014.11.004"},{"key":"S0022481220000729_r16","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(77)90004-3"},{"key":"S0022481220000729_r10","doi-asserted-by":"publisher","DOI":"10.1002\/malq.201500019"},{"key":"S0022481220000729_r22","doi-asserted-by":"publisher","DOI":"10.1201\/9781439865873-16"},{"key":"S0022481220000729_r9","doi-asserted-by":"publisher","DOI":"10.1215\/00294527-2010-030"},{"key":"S0022481220000729_r11","unstructured":"[11] Goldberg, G. , Can ${H}_{\\omega_1}$ and ${H}_{\\omega_2}$ be in bi-interpretation synonymy? MathOverflow answer, 2020. Available at https:\/\/mathoverflow.net\/q\/350585 (accessed 16 January, 2020)."},{"key":"S0022481220000729_r21","first-page":"183","article-title":"Toward model theory through recursive saturation","volume":"43","author":"Schlipf","year":"1978","journal-title":"Journal"},{"key":"S0022481220000729_r17","volume-title":"Encyclopedia of Mathematics and Its Applications","volume":"42","author":"Hodges","year":"1993"},{"key":"S0022481220000729_r23","doi-asserted-by":"publisher","DOI":"10.1017\/bsl.2019.15"},{"key":"S0022481220000729_r3","first-page":"99","volume-title":"Liber Amicorum Alberti: A Tribute to Albert Visser","author":"Enayat","year":"2016"},{"key":"S0022481220000729_r7","first-page":"1","article-title":"When bi-interpretability implies synonymy","volume":"320","author":"Friedman","year":"2014","journal-title":"Logic Group Preprint Series"},{"key":"S0022481220000729_r15","unstructured":"[15] Hamkins, J. D. , The real numbers are not interpretable in the complex field. Mathematics and Philosophy of the Infinite, 2020. Available at http:\/\/jdh.hamkins.org\/the-real-numbers-are-not-interpretable-in-thecomplex-field\/ (accessed 24 February, 2020)."},{"key":"S0022481220000729_r1","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-011-0264-5"},{"key":"S0022481220000729_r18","unstructured":"[18] Hamkins, J. D. and Seabold, D. , Well-founded Boolean ultrapowers as large cardinal embeddings, Mathematics and Philosophy of the Infinite, 2006, pp. 1\u201340. arXiv:1206.6075[math.LO]. Available at http:\/\/jdh.hamkins.org\/boolean-ultrapowers\/"},{"key":"S0022481220000729_r5","unstructured":"[5] Freire, A. R. , Estudo comparado do comprometimento ontol\u00f3gico das teorias de classes e conjuntos, Ph.D. thesis, University of Campinas, 2019."},{"key":"S0022481220000729_r14","unstructured":"[14] Hamkins, J. D. , Can ${H}_{\\omega_1}$ and ${H}_{\\omega_2}$ be in bi-interpretation synonymy? MathOverflow question, 2020. Available at https:\/\/mathoverow.net\/q\/350542 (accessed 16 January, 2020)."}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481220000729","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,18]],"date-time":"2022-02-18T11:16:51Z","timestamp":1645183011000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481220000729\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,30]]},"references-count":23,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["S0022481220000729"],"URL":"https:\/\/doi.org\/10.1017\/jsl.2020.72","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10,30]]},"assertion":[{"value":"\u00a9 The Association for Symbolic Logic 2020","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}