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dc.creatorFerreirós Domínguez, José Manuel
dc.date.accessioned2016-03-03T15:00:08Z
dc.date.available2016-03-03T15:00:08Z
dc.date.issued2011
dc.identifier.issn1079-8986
dc.identifier.urihttp://hdl.handle.net/11441/36830
dc.description.abstractSet theory deals with the most fundamental existence questions in mathematics– questions which affect other areas of mathematics, from the real numbers to structures of all kinds, but which are posed as dealing with the existence of sets. Especially noteworthy are principles establishing the existence of some infinite sets, the so-called “arbitrary sets.” This paper is devoted to an analysis of the motivating goal of studying arbitrary sets, usually referred to under the labels of quasi-combinatorialism or combinatorial maximalist. After explaining what is meant by definability and by “arbitrariness”, a first historical part discusses the strong motives why set theory was conceived as a theory of arbitrary sets, emphasizing connections with analysis and particularly with the continuum of real numbers. Judged from this perspective, the axiom of choice stands out as a most central and natural set-theoretic principle (in the sense of quasi-combinatorialism). A second part starts by considering the potential mismatch between the formal systems of mathematics and their motivating conceptions, and proceeds too fferan elementary discussion of how far the Zermelo–Fraenkel system goes in laying out principles that capture the idea of “arbitrary sets”. We argue that the theory is rather poor in this respect.es
dc.description.sponsorshipJunta de Andalucía P07-HUM-02594es
dc.description.sponsorshipMinisterio de Ciencia y Tecnología BFF2003-09579-C03es
dc.formatapplication/pdfes
dc.language.isoenges
dc.publisherAssociation for Symbolic Logic, Cambridge University Presses
dc.relation.ispartofThe Bulletin of Symbolic Logic, 17(3), 361-393es
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.titleOn arbitrary sets and ZFCes
dc.typeinfo:eu-repo/semantics/articlees
dc.type.versioninfo:eu-repo/semantics/publishedVersiones
dc.rights.accessrightsinfo:eu-repo/semantics/openAccesses
dc.contributor.affiliationUniversidad de Sevilla. Departamento de Filosofía y Lógica y Filosofía de la Cienciaes
dc.relation.projectIDP07-HUM-02594es
dc.relation.projectIDBFF2003-09579-C03es
dc.relation.publisherversionhttp://projecteuclid.org/download/pdf_1/euclid.bsl/1309952318es
dc.relation.publisherversionhttp://dx.doi.org/10.2178/bsl/1309952318
dc.identifier.doi10.2178/bsl/1309952318
dc.identifier.idushttps://idus.us.es/xmlui/handle/11441/36830
dc.contributor.funderJunta de Andalucía
dc.contributor.funderMinisterio de Ciencia y Tecnología (MCYT). España

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