Abstract: The notion of VC dimension, as appeared first in machine learning and later made its way to model theory, is a measure of complexity for families of subsets of a set X. In the upcoming series of talks, I will first give a detailed introduction to this notion, motivated by examples appearing throughout mathematics, and describe the model-theoretic significance of this notion. Later, I will discuss a paper of Bays, Ben-Neria, Kaplan and Simon, in which they prove a general result on so-called "NIP" first-order theories, namely, theories in which all definable families have finite VC-dimension. Finally, I will prove a result on the existence of cofinal families of finite subsets of aleph_n with finite VC dimension, answering a question which appeared in their paper, and discuss generalizations to other infinite cardinals.

This work is part of my Master's thesis, and is joint with Omer Ben-Neria and Itay Kaplan.

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George's talk will also be broadcasted on Zoom via the following link:https://huji.zoom.us/j/81343483264?pwd=ZTNhZmpGbC95dHpHSllMR1VYVXpzZz09

Meeting ID: 813 4348 3264
Passcode: 157589