M9260 Model theory

Faculty of Science
autumn 2017
Extent and Intensity
2/0/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Michael Joseph Lieberman, B.A., Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Jiří Rosický, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 18. 9. to Fri 15. 12. Tue 16:00–17:50 M4,01024
Prerequisites
Familiarity with predicate logic, basic abstract algebra, and naive set theory would be very helpful, but is not strictly required. The chief prerequisite is a level of mathematical maturity commensurate with an advanced undergraduate/graduate course.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
At the end of the course, students will be able to understand and apply the tools and techniques of modern model theory, including:
Logical compactness
Quantifier elimination
Saturated models
Fraisse limits
Omitting types, stability
Abstract independence, bases, and dimension
Syllabus
  • The main emphasis of the course will be on the following topics:
  • Similarity types, structures.
  • Completeness and compactness theorems, Lowenheim-Skolem theorem.
  • Construction of models from constants, Henkin's omitting types theorem, prime and atomic models.
  • Elementary chains of models, saturated models.
  • Quantifier elimination, model completeness.
  • Results on countable models, including Ryll-Nardzewski's theorem.
  • Stability (especially omega-stability), rank functions.
  • Indiscernible sequences, Ehrenfeucht-Mostowski models.
  • Morley's categoricity theorem.
  • Applications: algebraic geometry, number theory, analysis.
  • Additional topics may include:
  • Combinatorial set theory
  • Fraisse limits
  • Related categorical structures
Literature
    recommended literature
  • MARKER, David. Model theory : an introduction. New York: Springer, 2002, viii, 342. ISBN 0387987606. info
    not specified
  • HODGES, Wilfrid. A shorter model theory. Cambridge: Cambridge University Press, 1997, x, 310. ISBN 0521587131. info
  • BUECHLER, Steven. Essential stability theory. Berlin: Springer-Verlag, 1996, xiv, 355. ISBN 3540610111. info
Teaching methods
The course will consist of two hours of lecture each week, with optional biweekly problem sets to be completed outside of class.
Assessment methods
Students will be evaluated on the basis of one written exam, given during the middle of the term and completed outside of class, and a final oral exam, which will consist of a small number of problems, most of which will be selected at random from a list circulated to students before the beginning of the exam period.
Attendance will not be required for completion of the course, but is essential to the achievement of the course's objectives. Optional assignments will be handed out regularly but will not count towards a student's grade, although they will be corrected and returned promptly.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught only once.
Teacher's information
http://www.math.muni.cz/~lieberman/M5920P17.html
  • Enrolment Statistics (recent)
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