Peter Dybjer - Intuitionistic Type Theory - Lecture I

Explore the foundations of Intuitionistic Type Theory in this comprehensive lecture by Peter Dybjer, delivered as part of the Hausdorff Trimester Program: Types, Sets and Constructions. Delve into the historical context and key concepts of this mathematical framework, including types, applications, material systems, and type systems. Examine the role of recursion combinators, paper formats, and System E in the development of the theory. Investigate dependent types, existential quantification, and the concept of the universe within Intuitionistic Type Theory. Analyze free systems, the abortion of choice, and various models. Gain insights into the openness of this theoretical approach and its implications for mathematical reasoning and computation.

Introduction
Historical Intuitionistic Type Theory
Types
Application
Material System
Type System
Recursion Combinator
Paper Format
System E
Dependent Types
Existential Quantification
What is the Universe
Intuitionistic Type Theory
Free Systems
Abortion of Choice
Models
Openness