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Previous talks this semester:
19.12.2019 , 2.15 pm, room 105,
Maciej Malicki (Warsaw School of Economics, SGH),
Title: Continuous logic VI
Abstract:
In the final talk, I will define the notion of principal type, and prove the Ryll-Nardzewski theorem for continuous logic.
5.12.2019 , 2.15 pm, room 105,
Maciej Malicki (Warsaw School of Economics, SGH),
Title: Continuous logic V
Abstract:
In the fifth talk, I will finish discussing spaces of types, and take a look at the concept of definability in metric structures.
21.11.2019 , 2.15 pm, room 105,
Maciej Malicki (Warsaw School of Economics, SGH),
Title: Continuous logic IV
Abstract:
In the fourth talk, I will continue with saturated models, and homogeneous models. Then I will start discussing spaces of types.
7.11.2019 , 2.15 pm, room 105,
Maciej Malicki (Warsaw School of Economics, SGH),
Title: Continuous logic III
Abstract:
In the third talk, I will continue discussing ultraproducts, and their applications: compactness theorem and a characterization of axiomazatibility. Then I will move to homogeneous, and saturated models.
24.10.2019 , 2.15 pm, room 105,
Maciej Malicki (Warsaw School of Economics, SGH),
Title: Continuous logic II
Abstract:
In the second talk, I will discuss full sets of connectives, ultraproducts, and their applications: compactness theorem and axiomazatibility. If time pertmits, I will also prove the downward Lowenheim- Skolem theorem, and say something about saturated models.
10.10.2019 , 2.15 pm, room 105,
Maciej Malicki (Warsaw School of Economics, SGH),
Title: Continuous logic I
Abstract:"This series of talks will be devoted to a gentle introduction to continuous logic - a natural generalization of first-order logic that is suitable in studying mathematical objects equipped with a metric, e.g. Polish metric spaces and groups, Banach spaces, C*-algebras, etc. Continuous logic is surprisingly parallel to classical logic, and all fundamental concepts such as definable sets, algebraic sets, type spaces, quantifier elimination, omitting types, imaginaries, stability, etc., have their counterparts in this setting.
In the first talk, we will discuss the very basics: metric structures, signatures, connectives and quantifiers, truth values, theories, etc.
Literature: Ben Yaacov, Itai; Berenstein, Alexander; Henson, C. Ward; Usvyatsov, Alexander; Model theory for metric structures. Model theory with applications to algebra and analysis. Vol. 2, 315–427, London Math. Soc. Lecture Note Ser., 350, Cambridge Univ. Press, Cambridge, 2008.
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Talks in the second semester of 2018-19.
Talks in the first semester of 2018-19.
Talks in the second semester of 2017-18.
Talks in the first semester of 2017-18.
Talks in the second semester of 2016-17.
Talks in the first semester of 2016-17.
Talks in the second semester of 2015-16.
Talks in the first semester of 2015-16.
Talks in the second semester of 2014-15.
Talks in the first semester of 2014-15.
Talks in the second semester of 2013-14.
Talks in the first semester of 2013-14.
Talks in the second semester of 2012-13.
Talks in the first semester of 2012-13.
Talks in the second semester of 2011-12.
Talks in the first semester of 2011-12.
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