Thesis Defense
Alexander Berenbeim
UIC
Foundations for the Analysis of Surreal-valued genetic functions
Abstract: The surreal numbers are properly understood as the game values of combinatorial games, which can be recursively defined in terms of canonical sets of numbers. In this talk, we review the material from two earlier lectures where we described numbers-as-games, and laid the foundational work for defining genetic functions. After reviewing relevant definitions, we proceed to ask and answer the following two questions: 1) can the complexity of an arbitrary set of genetic function be uniformly bounded such that we can identify classes of models of these functions by truncating the surreal number at specific ordinals? 2) Are there non-trivial examples that emerge from this construction? To answer both of these questions, we introduce a pseudo-absolute value and a corresponding notion of Veblen rank, which we will use to uniformly bind the complexity of genetic functions, and show that the kappa and lambda maps that arise in the study of the Berarducci-Mantova derivative are of non-trivial Veblen rank.
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Alexander Michael Berenbeim is inviting you to a scheduled Zoom meeting.
Topic: Alexander Berenbeim's Dissertation Defense
Time: Oct 28, 2021 09:30 AM Central Time (US and Canada)
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Thursday October 28, 2021 at 9:30 AM in Zoom