FIT2.3.3. Algebraic Extensions
Field Theory: We define an algebraic extension of a field F and show that successive algebraic extensions are also algebraic. This gives a useful criterion for checking algberaic elements. We finish with algebraic closures.
From playlist Abstract Algebra
Thorsten Altenkirch - 1/2 Towards a Syntax for Cubical Type Theory
One of the key problems of Homotopy Type Theory is that it introduces axioms such as extensionality and univalence for which there is no known computational interpretation. We propose to overcome this by introducing a Type Theory where a heterogenous equality is defined recursively and equ
From playlist T2-2014 : Semantics of proofs and certified mathematics
Galois theory: Infinite Galois extensions
This lecture is part of an online graduate course on Galois theory. We show how to extend Galois theory to infinite Galois extensions. The main difference is that the Galois group has a topology, and intermediate field extensions now correspond to closed subgroups of the Galois group. We
From playlist Galois theory
Andrej Bauer and Peter LeFanu Lumsdaine: Toward an initiality theorem for general type theories
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: I will report on a project of defining carefully and formally what a general type theory is. This is kind of step 1 to a generally applicable initiality theorem. It's not
From playlist Workshop: "Types, Homotopy, Type theory, and Verification"
On the Setoid Model of Type Theory - Erik Palmgren
Erik Palmgren University of Stockholm October 18, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Working Group on Univalent Foundations - Michael Shulman
Michael Shulman Institute for Advanced Study December 12, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
There are two different types of reductionism. One is called methodological reductionism, the other one theory reductionism. Methodological reductionism is about the properties of the real world. It’s about taking things apart into smaller things and finding that the smaller things determ
From playlist Philosophy of Science
Field Theory: Let F be a subfield of the field K. We consider K as a vector space over F and define the degree of K over F as the dimension. We give a degree formula for successive extensions, and consider extensions in terms of bases. EDIT: Typo - around 3:15, it should be cube root(2
From playlist Abstract Algebra
Bas Spitters: Modal Dependent Type Theory and the Cubical Model
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: In recent years we have seen several new models of dependent type theory extended with some form of modal necessity operator, including nominal type theory, guarded and c
From playlist Workshop: "Types, Homotopy, Type theory, and Verification"
Tests, Games, and Martin-Lof's Meaning Explanations for Intuitionistic Type Theory - Peter Dybjer
Peter Dybjer November 30, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Martin Hötzel Escardó: Constructive Mathematics in Univalent Type Theory (Lecture II)
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions
From playlist HIM Lectures: Trimester Program "Types, Sets and Constructions"
Martin Hötzel Escardó: Constructive Mathematics in Univalent Type Theory (Lecture I)
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions
From playlist HIM Lectures: Trimester Program "Types, Sets and Constructions"
Live CEOing Ep 410: Language Design in Wolfram Language [Combinators]
In this episode of Live CEOing, Stephen Wolfram reviews the design of some upcoming functionality for the Wolfram Language. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or through the official Twitch channel of Stephen W
From playlist Behind the Scenes in Real-Life Software Design
Furio Honsell - Tribute to Ennio De Giorgi - 20 September 2016
Honsell, Furio "Implementing Cantor’s paradise in constructive type theory"
From playlist A Mathematical Tribute to Ennio De Giorgi
Toward a Computational Interpretation of Univalence - Daniel Licata
Daniel Licata Carnegie Mellon University; Member, School of Mathematics October 18, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
5 - Kick-off afternoon : Vladimir Voevodsky, Univalent Foundations
Vladimir Voevodsky (Institute for Advanced Study, Princeton): Univalent Foundations - new type-theoretic foundations of mathematics
From playlist T2-2014 : Semantics of proofs and certified mathematics
Zermelo Fraenkel Extensionality
This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. In this lecture we discuss the axiom of extensionality, which says that two sets are equal if they have the same elements. For the other lectures in the course see https://www.youtube.com/playlist?list
From playlist Zermelo Fraenkel axioms
This video is about extensions of fields.
From playlist Basics: Field Theory
Axiom of Choice and Regularity each imply LEM
I recommend you go through all parts, but thee AC-LEM proof starts at 55:30. If you skip stuff, still watch the section at 8:22, because I talk in terms of those semantics later. The Regularity-LEM proof at 1:50:55 requires definitions from the earlier AC-LEM proof. Timestamps: 0:00 Intro
From playlist Summer of Math Exposition 2 videos