The Absolute Model Companionship Spectrum of a Mathematical Theory and the Continuum Problem

Explore a comprehensive lecture on the (Absolute) Model Companionship Spectrum of mathematical theory and the Continuum problem, presented by Matteo Viale from the University of Torino and University of Turin. Delve into topics such as existentially closed models, absolute model companionship, strongly consistent replies, and counter examples. Examine key concepts including definitions, equality, equivalent propositions, model completeness, and modern companionship. Gain insights into unique freedom and its implications in set theory. This 1 hour and 27 minute seminar, hosted by the Fields Institute, offers an in-depth analysis of advanced mathematical concepts and their applications.

Introduction
Theory
Existentially closed models
Absolute model companionship
Strongly consistent reply
Counter example
Definition
Equality
Equivalent proposition
Model complete
Modern Companionship
Unique Freedom