Foundations 5: Intuitionistic Logic and Type Theory
In this series we develop an understanding of the modern foundations of pure mathematics, starting from first principles. We start with intuitive ideas about set theory, and introduce notions from category theory, logic and type theory, until we are in a position to understand dependent type theory, and in particular, homotopy type theory, which promises to replace set theory as the foundation of modern mathematics. We also take an interest in computer science, and how to write computer programming languages to formalize mathematics.
In this video we introduce a type theoretic description of Heying algebras/ intuitionistic logic. We prove a few important results about intuitionistic logic, and then informally introduce some more ideas from type theory.
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