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Randomizations of models as metric structures
- Source :
- Confluentes Mathematici 1, 2 (2009) 197-223
- Publication Year :
- 2009
-
Abstract
- The notion of a randomization of a first order structure was introduced by Keisler in the paper Randomizing a Model, Advances in Math. 1999. The idea was to form a new structure whose elements are random elements of the original first order structure. In this paper we treat randomizations as continuous structures in the sense of Ben Yaacov and Usvyatsov. In this setting, the earlier results show that the randomization of a complete first order theory is a complete theory in continuous logic that admits elimination of quantifiers and has a natural set of axioms. We show that the randomization operation preserves the properties of being omega-categorical, omega-stable, and stable.
- Subjects :
- Mathematics - Logic
03C45
03C90
03B50
03B48
Subjects
Details
- Database :
- arXiv
- Journal :
- Confluentes Mathematici 1, 2 (2009) 197-223
- Publication Type :
- Report
- Accession number :
- edsarx.0901.1583
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1142/S1793744209000080