Mathematical logic | Model theory

Type (model theory)

In model theory and related areas of mathematics, a type is an object that describes how a (real or possible) element or finite collection of elements in a mathematical structure might behave. More precisely, it is a set of first-order formulas in a language L with free variables x1, x2,…, xn that are true of a sequence of elements of an L-structure . Depending on the context, types can be complete or partial and they may use a fixed set of constants, A, from the structure . The question of which types represent actual elements of leads to the ideas of saturated models and omitting types. (Wikipedia).

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Natural Models of Type Theory - Steve Awodey

Steve Awodey Carnegie Mellon University; Member, School of Mathematics March 28, 2013 For more videos, visit http://video.ias.edu

From playlist Mathematics

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Model Theory - part 01 - The Setup in Classical Set Valued Model Theory

Here we give the basic setup for Model Theory. I learned this from a talk Tom Scanlon gave in 2010 at CUNY.

From playlist Model Theory

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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

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Model Theory - part 07 - Semantics pt 1

This is the first video on semantics.

From playlist Model Theory

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Christian Sattler: Do cubical models of type theory also model homotopy types

The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: I will give an alternative exposition of Kapulkin and Voevodsky's result about simplicial sets forming a subtopos of certain cubical sets: https://arxiv.org/abs/1805.0412

From playlist Workshop: "Types, Homotopy, Type theory, and Verification"

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Model Theory - part 04 - Posets, Lattices, Heyting Algebras, Booleans Algebras

This is a short video for people who haven't seen a Heyting algebras before. There is really nothing special in it that doesn't show up in wikipedia or ncatlab. I just wanted to review it before we use them. Errata: *at 3:35: there the law should read (a and (a or b) ), not (a and (a and

From playlist Model Theory

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Model Theory - part 03 - Terms, Formulas, Sequents

He we are a little bit more precise about keeping track of what fragments of formal languages we are using. This becomes relevant when you want to interpret them later. Caramello's book was useful in preparing this. We also found the post on nCatLab useful.

From playlist Model Theory

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A Practical Introduction to Interpretations.

We give a definition that is necessary for the construction of Hodge Theaters.

From playlist Model Theory

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The synthetic theory of ∞-categories vs the synthetic theory of ∞-categories - Emily Riehl

Vladimir Voevodsky Memorial Conference Topic: The synthetic theory of ∞-categories vs the synthetic theory of ∞-categories Speaker: Emily Riehl Affiliation: Johns Hopkins University Date: September 12, 2018 For more video please visit http://video.ias.edu

From playlist Mathematics

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Univalence from a computer science point-of-view - Dan Licata

Vladimir Voevodsky Memorial Conference Topic: Univalence from a computer science point-of-view Speaker: Dan Licata Affiliation: Wesleyan University Date: September 14, 2018 For more video please visit http://video.ias.edu

From playlist Mathematics

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Inernal Languages for Higher Toposes - Michael Shulman

Michael Shulman University of California, San Diego; Member, School of Mathematics October 3, 2012 For more videos, visit http://video.ias.edu

From playlist Mathematics

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String Theory and the Real World - S. Schafer-Nameki - 2/24/2015

Introduction by John Schwarz. Learn more about the Inaugural Celebration and Symposium of the Walter Burke Institute for Theoretical Physics: https://burkeinstitute.caltech.edu/workshops/Inaugural_Symposium Produced in association with Caltech Academic Media Technologies. ©2015 Californi

From playlist Walter Burke Institute for Theoretical Physics - Dedication and Inaugural Symposium - Feb. 23-24, 2015

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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

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Emily Riehl: On the ∞-topos semantics of homotopy type theory: All ∞-toposes have... - Lecture 3

HYBRID EVENT Recorded during the meeting "Logic and Interactions" the February 24, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual M

From playlist Topology

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Lecture 1: Invitation to topos theory

This talk introduces the motivating question for this semester of the Curry-Howard seminar, which is how to organise mathematical knowledge using topoi. The approach sketched out in the talk is via first-order theories, their associated classifying topoi, and adjoint pairs of functors betw

From playlist Topos theory seminar

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Random Matrices (Tutorial) by Spenta wadia

Statistical Physics Methods in Machine Learning DATE: 26 December 2017 to 30 December 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru The theme of this Discussion Meeting is the analysis of distributed/networked algorithms in machine learning and theoretical computer science in the

From playlist Statistical Physics Methods in Machine Learning

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Physics under the Gravitational Rainbow by Claudia de Rham

Program Cosmology - The Next Decade ORGANIZERS : Rishi Khatri, Subha Majumdar and Aseem Paranjape DATE : 03 January 2019 to 25 January 2019 VENUE : Ramanujan Lecture Hall, ICTS Bangalore The great observational progress in cosmology has revealed some very intriguing puzzles, the most i

From playlist Cosmology - The Next Decade

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Introduction to Classification Models

Ever wonder what classification models do? In this quick introduction, we talk about what classifications models are, as well as what they are used for in machine learning. In machine learning there are many different types of models, all with different types of outcomes. When it comes t

From playlist Introduction to Machine Learning

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