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Lecture Notes | Itay Kaplan

Lecture Notes

 

These are some notes of courses that I’m teaching or have taught in the Hebrew University.

Logic 1 (80423) (Winter 2019). This course is the basic course in mathematical logic, presenting Gödel’s completeness theorem and related subjects. The lecture notes are in Hebrew; if you already know logic, you can use this opportunity to learn Hebrew.

Logic 2 (80424) (Spring 2020). This course is about Gödel’s incompleteness theorems and related subjects, including an introduction to recursion theory.

Basic set theory (80200) (Spring 2022).

Model theory and homogeneous structures (80645). This course covers selected topics from the model theory of homogeneous structures such as omega-categoricityFraïssé limits, generic automorphisms, interpretations, ample generics, the small index property, and Ramsey theory.

Model theory 1+2 (80616, 80824) (2017-18). This course starts from a basic introduction to model theory, goes through the Baldwin-Lachlan proof of Morley’s theorem, and ends with general stability theory and some applications.

Introduction to forcing (80579) (2017). This course covers the basics of forcing. It concludes with a proof of the consistency of Martin’s Axiom.

Geometric stability theory (80896) (2020-2021). The original goal of this course was to analyze totally- categorical theories, but fell short on this, and instead covered some parts of geometric stability theory, mostly following Martin Bays’ notes, culminating in the proof that any unimodular minimal set is locally modular.