Mathematical logic | Model theory | Theorems in the foundations of mathematics
In mathematical logic, a theory is categorical if it has exactly one model (up to isomorphism). Such a theory can be viewed as defining its model, uniquely characterizing its structure. In first-order logic, only theories with a finite model can be categorical. Higher-order logic contains categorical theories with an infinite model. For example, the second-order Peano axioms are categorical, having a unique model whose domain is the set of natural numbers In model theory, the notion of a categorical theory is refined with respect to cardinality. A theory is κ-categorical (or categorical in κ) if it has exactly one model of cardinality κ up to isomorphism. Morley's categoricity theorem is a theorem of Michael D. Morley stating that if a first-order theory in a countable language is categorical in some uncountable cardinality, then it is categorical in all uncountable cardinalities. Saharon Shelah extended Morley's theorem to uncountable languages: if the language has cardinality κ and a theory is categorical in some uncountable cardinal greater than or equal to κ then it is categorical in all cardinalities greater than κ. (Wikipedia).
Model Theory - part 07 - Semantics pt 1
This is the first video on semantics.
From playlist Model Theory
IAML2.7: Categorical (nominal) attributes
From playlist Thinking about Data
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than
From playlist Physics
Giuseppe Rosolini: Categorical completions in constructive mathematics
The lecture was held within the framework of the Hausdorff Trimester Program: Constructive Mathematics. Abstract: There seems to be a very close connection between category theory and constructive mathematics which still is hard to make manifest, but which may be extremely useful to impr
From playlist Workshop: "Constructive Mathematics"
Chris Stewart (Pt. 1) - Aesthetic Cognitivism: Overview & Concepts
Free access to Closer to Truth's library of 5,000 videos: http://bit.ly/2UufzC7 Aesthetic Cognitivism is a theory about the value of the arts as sources of understanding—the arts as more than sources of delight, amusement, pleasure, or emotional catharsis (though they can certainly be all
From playlist Aesthetic Cognitivism: Overview & Concepts - CTT Interview Series
The Nature of Causation: The Counterfactual Theory of Causation
In this second lecture in this series on the nature of causation, Marianne Talbot discusses the counterfactual theory of causation. We have causal theories of reference, perception, knowledge, content and numerous other things. If it were to turn out that causation doesn’t exist, we would
From playlist The Nature of Causation
Categorical actions in geometry and representation theory - Clemens Koppensteiner
Short talks by postdoctoral members Topic: Categorical actions in geometry and representation theory Speaker: Clemens Koppensteiner Affiliation: Member, School of Mathematics Date: September 29, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Logic: The Structure of Reason
As a tool for characterizing rational thought, logic cuts across many philosophical disciplines and lies at the core of mathematics and computer science. Drawing on Aristotle’s Organon, Russell’s Principia Mathematica, and other central works, this program tracks the evolution of logic, be
From playlist Logic & Philosophy of Mathematics
How to diagonalize a functor - Benjamin Elias
Members' Seminar Topic: How to diagonalize a functor Speaker: Benjamin Elias Affiliation: University of Oregon; von Neumann Fellow, School of Mathematics Date: October 5, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Huawei Young Talents Programme - Laurent Lafforgue
The online ceremony celebrating the official launch of the Huawei Young Talents Program at the Institut des Hautes Etudes Scientifiques was held on 6 November 2020. This program aims to support the work of talented researchers in mathematics and theoretical physics at the beginning of thei
From playlist Huawei Young Talents Program - November 2020
Saharon Shelah : Categoricity of atomic classes in small cardinals, in ZFC
CONFERENCE Recording during the thematic meeting : « Discrete mathematics and logic: between mathematics and the computer science » the January 17, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks give
From playlist Logic and Foundations
Tom Leinster : The categorical origins of entropy
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 29, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Geometry
Towards elementary infinity-toposes - Michael Shulman
Vladimir Voevodsky Memorial Conference Topic: Towards elementary infinity-toposes Speaker: Michael Shulman Affiliation: University of San Diego Date: September 13, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
On finite dimensional omega-categorical structures (...) - P. Simon - Workshop 1 - CEB T1 2018
Pierre Simon (Berkeley) / 31.01.2018 On finite dimensional omega-categorical structures and NIP theories The study of omega-categorical structures lies at the intersection of model theory, combinatorics and group theory. Some classes of omega-categorical structures have been classified,
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Social Identity Theory - Definition + 3 Components
Learn more about Henri Tajfel's Social Identity Theory: https://practicalpie.com/social-identity-theory/ Enroll in my 30 Day Brain Bootcamp: https://practicalpie.com/30-day-brain-bootcamp-plan/ --- Invest in yourself and support this channel! --- ❤️ Psychology of Attraction: https://prac
From playlist Social Psychology
LambdaConf 2015 - Type Theory and its Meaning Explanations Jon Sterling
At the heart of intuitionistic type theory lies an intuitive semantics called the “meaning explanations." Crucially, when meaning explanations are taken as definitive for type theory, the core notion is no longer “proof” but “verification”. We’ll explore how type theories of this sort aris
From playlist LambdaConf 2015
Galois theory: Transcendental extensions
This lecture is part of an online graduate course on Galois theory. We describe transcendental extension of fields and transcendence bases. As applications we classify algebraically closed fields and show hw to define the dimension of an algebraic variety.
From playlist Galois theory
Clemens Koppensteiner: T-structures from categorical actions
Abstract: T-structures on derived categories of coherent sheaves are an important tool to encode both representation-theoretic and geometric information. Unfortunately there are only a limited amount of tools available for the constructions of such t-structures. We show how certain geometr
From playlist Algebraic and Complex Geometry
Quantum Theory - Full Documentary HD
Check: https://youtu.be/Hs_chZSNL9I The World of Quantum - Full Documentary HD http://www.advexon.com For more Scientific DOCUMENTARIES. Subscribe for more Videos... Quantum mechanics (QM -- also known as quantum physics, or quantum theory) is a branch of physics which deals with physica
From playlist TV Appearances
R & Python - Conditional Inference Trees
Lecturer: Dr. Erin M. Buchanan Summer 2020 https://www.patreon.com/statisticsofdoom This video is part of my human language modeling class - this video set covers the updated version with both R and Python. This video explores the use of conditional inference trees and random forests to
From playlist Human Language (ANLY 540)