MATH 282C LEC A: MODEL THEORY (45580)

Instructor Contact Information:

Isaac Goldbring
Email: isaac@math.uci.edu

Homepage: http://www.math.uci.edu/􏰀isaac
Office Hours: By appointment.

Course Information:

• There will be no required text.  Here is a list of sources that I will often borrow from or cite:

  • Model theory for metric structures Links to an external site. by A. Berenstein, I. Ben-Yaacov, C.W. Henson, and A. Usvyatsov
  • Continuous first order logic and local stability Links to an external site. by I. Ben-Yaacov and A. Usvyatsov
  • Course lecture notes on continuous model theory and applications Links to an external site. by B. Hart

• Class Meetings: There are three hours of lecture a week: MWF 9-9:50 to be held by Zoom (Zoom invitation to be emailed)

• Your entire grade will be determined by a 50 minute presentation on the topic of your choice to be given during the final two weeks of the quarter.  Beamer presentations strongly encouraged.  You must communicate your choice to me by the end of Week 5.  Here is a list of suggested topics:
  • Model theory of the Gurarij Banach space (see this paper Links to an external site. by I. Ben-Yaacov and C.W. Henson)
  • Model theory of the Urysohn space (see these slides Links to an external site. by B. Hart or Section 5 of this paper by C. Ealy and I. Goldbring)
  • Model theory and ergodic theory (see, for example, this paper Links to an external site. by T. Iberlucia and T. Tsankov)
  • Randomizations of structures (see this paper Links to an external site. by I. Ben-Yaacov and H. Jerome Keisler)
  • Model theory of operator algebras (this is a massive and very active area of research, so if you want to speak about this and do not know where to start, let me know)
  • The almost-sure theory of finite metric spaces (see this paper Links to an external site. by I. Goldbring, B. Hart, and A. Kruckman)
  • Ehrenfeucht-Fraisse Games in continuous logic (see these slides Links to an external site. by B. Hart and their continuation Links to an external site.)