A System of Axioms for Minkowski Spacetime.
We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in Maudlin (2012) and Malament (un...
| Publicado en: | Journal of Philosophical Logic Vol. 50; no. 1; pp. 149 - 186 |
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| Autores principales: | , |
| Formato: | Artículo |
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Springer Nature
2021
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| Materias: | |
| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=148190161&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 148190161 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00223611 JPH jtl: Journal of Philosophical Logic issn: 00223611 maglogo: N pubinfo: dt: 2021 vid: 50 iid: 1 pid: 237 pub: Springer Nature artinfo: ui: 148190161 10.1007/s10992-020-09565-6 ppf: 149 ppct: 37 formats: fmt: @attributes: type: P size: 2MB tig: atl: A System of Axioms for Minkowski Spacetime. aug: au: Cocco, Lorenzo Babic, Joshua affil: Department of Philosophy, University of Geneva, Geneva, Switzerland su: Pythagorean theorem Spacetime Mathematical logic Axioms Minkowski geometry First-order logic sug: subj: Pythagorean theorem Spacetime Mathematical logic Axioms Minkowski geometry First-order logic keyword: Axiomatization Minkowski spacetime Nominalism Representation theorems Special relativity Synthetic mechanics and geometry ab: We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in Maudlin (2012) and Malament (unpublished). It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of Tarski (1959): a predicate of betwenness and a four place predicate to compare the square of the relativistic intervals. Minkowski spacetime is described as a four dimensional 'vector space' that can be decomposed everywhere into a spacelike hyperplane—which obeys the Euclidean axioms in Tarski and Givant (The Bulletin of Symbolic Logic, 5(2), 175–214 1999)—and an orthogonal timelike line. The length of other 'vectors' are calculated according to Pythagoras' theorem. We conclude with a Representation Theorem relating models M of our system M 1 that satisfy second order continuity to the mathematical structure 〈 ℝ 4 , η a b 〉 , called 'Minkowski spacetime' in physics textbooks. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Journal of Philosophical Logic is a copyright of Springer, 2021. All Rights Reserved. item: Journal of Philosophical Logic holder: Springer Nature dt: @attributes: year: 2021 holdings: @attributes: islocal: N |
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