SEPARABLE MODELS OF RANDOMIZATIONS.
Every complete first order theory has a corresponding complete theory in continuous logic, called the randomization theory. It has two sorts, a sort for random elements of models of the first order theory, and a sort for events. In this paper we establish connections between properties of countable...
| Publicado en: | Journal of Symbolic Logic Vol. 80; no. 4; pp. 1149 - 1182 |
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| Autores principales: | , |
| Formato: | Artículo |
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Cambridge University Press
Dec2015
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| 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=111900133&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 111900133 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00224812 3TY jtl: Journal of Symbolic Logic issn: 00224812 maglogo: N pubinfo: dt: Dec2015 vid: 80 iid: 4 pid: 15979 pub: Cambridge University Press artinfo: ui: 111900133 10.1017/jsl.2015.33 ppf: 1149 ppct: 33 formats: tig: atl: SEPARABLE MODELS OF RANDOMIZATIONS. aug: au: ANDREWS, URI KEISLER, H. JEROME affil: DEPARTMENT OF MATHEMATICS UNIVERSITY OF WISCONSIN-MADISON MADISON, WI, 53706, USA su: Separable algebras Set theory Random variables Ordered groups Isomorphism (Mathematics) sug: subj: Separable algebras Set theory Random variables Ordered groups Isomorphism (Mathematics) keyword: 03B50 03C40 continuous model theory metric structure Primary 03C15 randomization Secondary 03C20 ab: Every complete first order theory has a corresponding complete theory in continuous logic, called the randomization theory. It has two sorts, a sort for random elements of models of the first order theory, and a sort for events. In this paper we establish connections between properties of countable models of a first order theory and corresponding properties of separable models of the randomization theory. We show that the randomization theory has a prime model if and only if the first order theory has a prime model. And the randomization theory has the same number of separable homogeneous models as the first order theory has countable homogeneous models. We also show that when T has at most countably many countable models, each separable model of TR is uniquely characterized by a probability density function on the set of isomorphism types of countable models of T. This yields an analogue for randomizations of the results of Baldwin and Lachlan on countable models of ω1-categorical first order theories. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y dt: @attributes: year: 2015 holdings: @attributes: islocal: N |
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