MAT8070-01 (2016학년도 1학기)

2016-01-30 02:33:45  2016-02-02 23:15:22 
논리학 특강 I 
과254  화6,7,8 
 
   
   
 
All students interested in mathematical logic
Introduction to stability theory and some generalizations such as the NIP thoery
No prerequisite
3 hours of lecture and 1 hour problem session weekly
Grades will be based on exams and solving the problems from problem lists
Dr Jan Dobrowolski, postdoctoral researcher
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Available above
2016-03-02 2016-03-08
Stable theories - definition, characterizations, examples 
Some characterizations of stability, superstability, omega-stability 
(3.2) Spring semester classes begin (3.4 - 3.8) Course add and drop period 
2016-03-09 2016-03-15
Basic properties of stable theories 
Properties of forking and dividing, open mapping theorem 
 
2016-03-16 2016-03-22
Ranks 
Morley rank, U-rank, local ranks 
 
2016-03-23 2016-03-29
More on ranks 
Properties of ranks in various classes of theories, connections with forking independence 
 
2016-03-30 2016-04-05
Canonical bases 
Definition and properties of canonical bases 
 
2016-04-06 2016-04-12
Modules as (stable) first-order structures 
Description of formulas in theories of modules, stability of modules 
(4.4 - 4.6) Course withdrawal period, (4.8) First third of the semester ends 
2016-04-13 2016-04-19
Pregeometries in regular types and types of U-rank 1 
Various geometric properties of pregeometries, characterizations of local modularity 
(4.18 - 4.22) Midterm examinations 
2016-04-20 2016-04-26
Stable groups 
Chain conditions, connected components. 
(4.18 - 4.22) Midterm examinations 
2016-04-27 2016-05-03
Stable groups (continued) 
Indecomposability theorem, interpretability of rings and fields 
 
10  2016-05-04 2016-05-10
NIP theories - basic properties 
Some equivalent characterizations. Witnessing by a formula in a single variable. 
(5.5)Children`s Day 
11  2016-05-11 2016-05-17
Examples of NIP theories 
o-minimal and weakly o-minimal theories, algebraically closed valued fields 
(5.14) foundation day Buddha`s Birthday, (5.16) Two thirds of the semester ends 
12  2016-05-18 2016-05-24
More on o-minimality 
Overview of problems related to o-minimal structures 
 
13  2016-05-25 2016-05-31
Measures in NIP theories 
General properties of Keisler measures: smoothness, invariance. 
 
14  2016-06-01 2016-06-07
Measures in NIP theories (continuation) 
Application of Keisler measures in the context of NIP (and more particular, o-minimal) structures 
(6.6) Memorial Day 
15  2016-06-08 2016-06-14
NIP groups 
Particular attention will be given to fsg groups 
(6.8 - 6.21) Self-Study and Final examinations Period 
16  2016-06-15 2016-06-21
Connections to topological dynamics 
S_G(M) as a G-flow, overview of some related results 
(6.8 - 6.21) Self-Study and Final examinations Period