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Metric Scott analysis
- Speaker(s)
- Todor Tsankov
- Affiliation
- Université Paris Diderot
- Date
- April 6, 2016, 4:15 p.m.
- Room
- room 5050
- Seminar
- Topology and Set Theory Seminar
Back-and-forth equivalence relations have been an important tool in
model theory and descriptive set theory since their advent in the fifties. They provide Borel approximations to the isomorphism relation that are useful in a variety of settings and are particularly important in infinitary model theory. In this work, we extend the theory to metric structures and describe the connections with infinitary continuous logic. Many classical results have a continuous counterpart (for example, the existence of Scott rank, the Lopez-Escobar theorem, etc.) but also new features appear that have no analogue in the classical setting and allow the study of equivalence relations other than isomorphism. This is joint work with I. Ben Yaacov, M. Doucha, and A. Nies.
model theory and descriptive set theory since their advent in the fifties. They provide Borel approximations to the isomorphism relation that are useful in a variety of settings and are particularly important in infinitary model theory. In this work, we extend the theory to metric structures and describe the connections with infinitary continuous logic. Many classical results have a continuous counterpart (for example, the existence of Scott rank, the Lopez-Escobar theorem, etc.) but also new features appear that have no analogue in the classical setting and allow the study of equivalence relations other than isomorphism. This is joint work with I. Ben Yaacov, M. Doucha, and A. Nies.
