Mathematical logic | Model theory

In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the statements of the theory hold). The aspects investigated include the number and size of models of a theory, the relationship of different models to each other, and their interaction with the formal language itself. In particular, model theorists also investigate the sets that can be defined in a model of a theory, and the relationship of such definable sets to each other.As a separate discipline, model theory goes back to Alfred Tarski, who first used the term "Theory of Models" in publication in 1954.Since the 1970s, the subject has been shaped decisively by Saharon Shelah's stability theory. Compared to other areas of mathematical logic such as proof theory, model theory is often less concerned with formal rigour and closer in spirit to classical mathematics.This has prompted the comment that "if proof theory is about the sacred, then model theory is about the profane".The applications of model theory to algebraic and diophantine geometry reflect this proximity to classical mathematics, as they often involve an integration of algebraic and model-theoretic results and techniques. The most prominent scholarly organization in the field of model theory is the Association for Symbolic Logic. (Wikipedia).

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

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

Model Theory - part 07 - Semantics pt 1

This is the first video on semantics.

From playlist Model Theory

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

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

A Practical Introduction to Interpretations.

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

From playlist Model Theory

Model Theory - part 02 - Signatures, Lawvere Categories, Structures (now valued in Categories!)

I learned about this approach from Riehl in the existential context here. Her webpage is here: http://www.math.jhu.edu/~eriehl/ Also, I found the refrences by Caramello and Awodey very helpful. They build on what is done in Reyes-Makkai. Whatever Awodey writes is basically gold. Here he

From playlist Model Theory

Model Theory - part 08 - Syntactic Catgories

These are the categories where functors from these dudes are models... these take forever to define. On top of it, these end up just being friggin' definable sets and definable morphisms!! I remember being a place in here where there is a diagram which i say commutes but I need to actually

From playlist Model Theory

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

Absolute notions in model theory - M. Dzamonja - Workshop 1 - CEB T1 2018

Mirna Dzamonja (East Anglia) / 30.01.2018 The wonderful theory of stability and ranks developed for many notions in first order model theory implies that many model theoretic constructions are absolute, since they can be expressed in terms of internal properties measurable by the existenc

From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields

Matrix Models, Gauge-Gravity Duality and Simulations on the Lattice by Georg Bergner

PROGRAM NONPERTURBATIVE AND NUMERICAL APPROACHES TO QUANTUM GRAVITY, STRING THEORY AND HOLOGRAPHY (HYBRID) ORGANIZERS: David Berenstein (University of California, Santa Barbara, USA), Simon Catterall (Syracuse University, USA), Masanori Hanada (University of Surrey, UK), Anosh Joseph (II

From playlist NUMSTRING 2022

CDIS 4017 - Models of Speech Production Part 1 (Done)

Chaya Guntupalli (Nanjundeswaran) Ph.D. CDIS 4017 - Speech and Hearing Science I ETSU Online Programs - http://www.etsu.edu/online

From playlist ETSU: CDIS 4017 - Speech and Hearing Science I | CosmoLearning Audiology

Inflation and Supergravity - A. Linde - 5/17/2014

Workshop on Primordial Gravitational Waves and Cosmology (May 16 - 17, 2014) Learn more about this workshop: http://burkeinstitute.caltech.edu/workshops Produced in association with Caltech Academic Media Technologies. © 2014 California Institute of Technology

From playlist Walter Burke Institute for Theoretical Physics - Workshop on Primordial Gravitational Waves and Cosmology (May 16 - 17, 2014)

Abraham Robinson’s legacy in model theory and (...) - L. Van den Dries - Workshop 3 - CEB T1 2018

Lou Van den Dries (University of Illinois, Urbana) / 27.03.2018 Abraham Robinson’s legacy in model theory and its applications ---------------------------------- Vous pouvez nous rejoindre sur les réseaux sociaux pour suivre nos actualités. Facebook : https://www.facebook.com/InstitutHe

From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields

The Large SpeNta Limit by David Gross

11 January 2017 to 13 January 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru String theory has come a long way, from its origin in 1970's as a possible model of strong interactions, to the present day where it sheds light not only on the original problem of strong interactions, but

From playlist String Theory: Past and Present

Kavli Distinguished Lecture SPEAKER: David Gross (KITP - University of California, Santa Barbara) DATE & TIME: 08 January 2018, 09:00 to 10:30 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru Abstract: A perspective on large N theories: their role in quantum field theory, in gauge-gravit

From playlist Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology 2018

Qubit Regularization of Asymptotic Freedom by Shailesh Chandrasekharan

PROGRAM Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography (ONLINE) ORGANIZERS: David Berenstein (UCSB), Simon Catterall (Syracuse University), Masanori Hanada (University of Surrey), Anosh Joseph (IISER, Mohali), Jun Nishimura (KEK Japan), David Sc

From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography (Online)

Washington Taylor - How Natural is the Standard Model in the String Landscape?

Mike's pioneering work in taking a statistical approach to string vacua has contributed to an ever-improving picture of the landscape of solutions of string theory. In this talk, we explore how such statistical ideas may be relevant in understanding how natural different realizations of th

From playlist Mikefest: A conference in honor of Michael Douglas' 60th birthday

Sebastian Reich (DDMCS@Turing): Learning models by making them interact

Complex models in all areas of science and engineering, and in the social sciences, must be reduced to a relatively small number of variables for practical computation and accurate prediction. In general, it is difficult to identify and parameterize the crucial features that must be incorp

From playlist Data driven modelling of complex systems