An axiomatic foundation of relativistic spacetime.
An ab-initio foundation for relativistic spacetime is given, which is a conservative extension of Zermelo's set theory with urelemente. Primitive entities are worldlines rather than spacetime points. Spacetime points are sets of intersecting worldlines. By the proper axioms, they form a manifold. En...
| Published in: | Synthese Vol. 192; no. 7; pp. 2009 - 2025 |
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| Format: | Article |
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Springer Nature
Jul2015
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| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=109574774&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 109574774 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Jul2015 vid: 192 iid: 7 pid: 237 pub: Springer Nature artinfo: ui: 109574774 10.1007/s11229-013-0345-6 ppf: 2009 ppct: 16 formats: fmt: @attributes: type: P size: 425KB tig: atl: An axiomatic foundation of relativistic spacetime. aug: au: Benda, Thomas affil: Institute of Philosophy of Mind, National Yang Ming University, Taipei Taiwan su: General relativity (Physics) Axiomatic set theory First-order logic Mathematical logic Spacetime sug: subj: General relativity (Physics) Axiomatic set theory First-order logic Mathematical logic Spacetime keyword: Axiomatization General relativity Set-theory ab: An ab-initio foundation for relativistic spacetime is given, which is a conservative extension of Zermelo's set theory with urelemente. Primitive entities are worldlines rather than spacetime points. Spacetime points are sets of intersecting worldlines. By the proper axioms, they form a manifold. Entities known in differential geometry, up to a metric, are defined and have the usual properties. A set-realistic point of view is adopted. The intended ontology is a set-theoretical hierarchy with a broad base of the empty set and urelemente. Sets generated from the empty set are mathematically interpreted, all other sets are physically interpreted. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2015. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2015 holdings: @attributes: islocal: N |
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