- published: 18 Dec 2012
- views: 3450
In mathematics, model theory is the study of classes of mathematical structures (e.g. groups, fields, graphs, universes of set theory) from the perspective of mathematical logic. The objects of study are models of theories in a formal language. We call a set of sentences in a formal language a theory; a model of a theory is a structure (e.g. an interpretation) that satisfies the sentences of that theory.
Model theory recognises and is intimately concerned with a duality: It examines semantical elements (meaning and truth) by means of syntactical elements (formulas and proofs) of a corresponding language. To quote the first page of Chang & Keisler (1990):
Model theory developed rapidly during the 1990s, and a more modern definition is provided by Wilfrid Hodges (1997):
although model theorists are also interested in the study of fields. Other nearby areas of mathematics include combinatorics, number theory, arithmetic dynamics, analytic functions, and non-standard analysis.
In a similar way to proof theory, model theory is situated in an area of interdisciplinarity among mathematics, philosophy, and computer science. The most prominent professional organization in the field of model theory is the Association for Symbolic Logic.
Model theory (thought not described as such in the book) is a method of description used in the "freshperson" maths book from 1960, Birkhoff and Maclane's "A Survey of Modern Algebra". For example, a group is described as a set of elements together with a set of operations on them. Birkhoff and Maclane define the concept of "relation". A function is a particular case of a relation. It is not surprising that this concept of relation was adopted by some computer writers, since many of these people would have studied treatments of maths similar to Birkhoff and Maclane. Without the work of Tarski, it is no doubt correct that Birkhoff and Maclane's book would have not been written in the form it was. If the word "relation" has not beeN used in maths books in 1960, it seems very likely th...
A brief intro to the current theory of (almost) everything - the Standard Model of particle physics. It's like cake, only universal. minutephysics is now on Google+ - http://bit.ly/qzEwc6 And facebook - http://facebook.com/minutephysics And twitter - @minutephysics Minute Physics provides an energetic and entertaining view of old and new problems in physics -- all in a minute! Music by Nathaniel Schroeder NEW ALBUM!! -- http://juliansaporiti.bandcamp.com/album/lusitania youtube: http://bit.ly/pakJLE Thanks to Nima Doroud and Alex Yale for contributions and to Perimeter Institute for support. Created by Henry Reich
Speaker: Boris Zilber (University of Oxford) Title: On model theory, noncommutative geometry and physics Event: Categories, Logic and Foundations of Physics VI (March 2010, University of Oxford) Abstract: Studying possible relations between a mathematical structure and its description in a formal language Model Theory developed a hierarchy of a 'logical perfection'. On the very top of this hierarchy we discovered a new class of structures called Zariski geometries. A joint theorem by Hrushovski and the speaker (1993) indicated that the general Zariski geometry looks very much like an algebraic variety over an algebraically closed field, but in general is not reducible to an algebro-geometric object. Later the present speaker established that a typical Zariski geometry can be explained in...
What is a model/theory, and why do economists use them? "EPISODE 5A: Models and Theories" by Dr. Mary J. McGlasson is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
You can directly support Crash Course at http://www.subbable.com/crashcourse Subscribe for as little as $0 to keep up with everything we're doing. Also, if you can afford to pay a little every month, it really helps us to continue producing great content. How did we get here? Well, in terms of Atomic Chemistry, Hank takes us on a tour of the folks that were part of the long chain of other folks who helped us get to these deeper understandings of the world. From Leucippus to Heisenberg to you - yes, YOU - the story of Atomic Chemistry is all wibbly-wobbly... and amazing. -- Table of Contents Leucippus, Democritus & Atomic Theory 0:09 Discharge Tubes 1:52 Ernest Rutherford & The Nucleus 4:22 Chemistry = Math 7:22 Niels Bohr Model 5:32 Heisenburg & Quantum Theory 6:35 -- Want to find Crash...
The Theory of Everything Soundtrack by Jóhann Jóhannsson
This video will describe the history of the atom starting with Democritus and Aristotle all the way to Erwin Schrodinger and Louis De Broglie
In this video you will learn the theory of Moving average model (MA) http://www.analyticuniversity.com/
Listen to the full audiobook: http://downloadapp.us/mabk/30/en/B01106NK1S/book Model of the Etheric Physiological Structure of the Body is presented in 2 parts: 1. A Common Theory of Oriental Medicine. An Integral Model for the System of Acupuncture Channels. A Common Theory of Chinese, Indian and Iranian medicines is presented on the basis of a model for the system of acupuncture channels. Applying the graphic description method to the system reveals new additional functional links; in particular, 4 new extra channels and plausible master points for their activation. 2. Model of Chakras System. Chakras and Acupuncture Channels. Model of Chakras System is related to the intercommunication between central (chakras system) and peripheral (meridians system) parts of the body. The model descri...
Filmed LIVE @ Sonic Bloom 2016 - http://sonicbloomfestival.com/ Jamie Janover is recognized as a true innovator & delegate of the Resonance Academy. He has lectured on Nassim Haramein’s Unified Field Theory across the USA & internationally. Jamie is also a master of the ancient percussion stringed instrument called the hammered dulcimer and even invented and performed on an instrument he calls the “mini-kit” (a miniature amplified drum kit). http://jamiejanover.com/ The Resonance Science Foundation & Resonance Academy is dedicated to advancing the research and education of Unified Physics and the unification of all sciences in alignment with a worldview of interconnection and wholeness. Their mission is to share the scientific knowledge and insights that arise from a unified view of the d...
Lecture 2 in a series of 21 lectures on solid state physics, delivered by Professor Steven H. Simon in early 2014. Creative Commons Attribution-Non-Commercial-Share Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/
Read your free e-book: http://appgame.space/mebk/50/en/B00DSLSVO0/book The Mental Models Theory of Reasoning presents theoretical and empirical research on an area of growing interest, the status of mental models in deductive reasoning. As research in the framework of the mental models theory flourishes, this book answers a need to assess the contribution of the notion of training and content. It covers the central issues of propositional, relational, causal and probabilistic reasoning, and argumentation and development. In addition, this work presents data regarding strategies, argumentation, and the development of reasoning. Special features of this text include:*sharp theoretical analyses as well as important new empirical data offered by theorists who work in the framework of the menta...
Read your free e-book: http://hotaudiobook.com/mebk/50/en/B00S3FBYUO/book This book aims to provide a description of these new Artificial Intelligence technologies and approaches to the modeling and simulation of complex systems, as well as an overview of the latest scientific efforts in this field such as the platforms and/or the software tools for smart modeling and simulating complex systems. These tasks are difficult to accomplish using traditional computational approaches due to the complex relationships of components and distributed features of resources, as well as the dynamic work environments. In order to effectively model the complex systems, intelligent technologies such as multi-agent systems and smart grids are employed to model and simulate the complex systems in the areas of...
A detailed online course on Networking Communication Protocols: Episode2 - OSI Model and its Theory vs Reality. Refer: https://en.wikipedia.org/wiki/OSI_model http://www.webopedia.com/quick_ref/OSI_Layers.asp http://computer.howstuffworks.com/osi1.htm http://www.studytonight.com/computer-networks/complete-osi-model If you are from Bangaluru and interested to join Summer classes on Networking, Linux, Systems software and software architecture you can contact me via email: kiran -dot- kankipati -at- gmail.com by Kiran Kankipati, Founder: TOFFEE Website: http://www.the-toffee-project.org --------------- Please do subscribe to this channel for live updates of upcoming episodes. Post your queries/clarifications on Youtube comments and get clarified :)
1D/2D hydraulic modeling, OpenMI Bert Jagers (DELTARES), Quillon Harpham (HRW) DRIHM Summer School Hydro-‐meteorological modelling using e Science environments 22- 25 September 2014 Master School of Civil Engineering Technical University of Madrid. The DRIHM project organizes the DRIHM Summer School 2014 on Hydro-meteorological modelling using e-Science environments, the school takes place from September 22nd until September 25th 2014 at the Civil Engineering School of the Technical University of Madrid. Attending the summer school is free of charge, including lecture notes and lunches. Vídeo producido por el Gabinete de Tele-Educación de la Universidad Politécnica de Madrid
Martin Zeman (University of California, Irvine) A panoramic view of inner model theory for not so small/large cardinals
In this lecture, instructor John Melton explains the theory of mind, a model used to illustrate how the mind works on the conscious and subconscious levels, how hypnosis occurs and how to create the hypnotic state. This clip is from the "Foundations in Hypnotherapy" course, which can be viewed in its' entirety at no charge by visiting www.hypnosis.edu/training
Anuj Dawar, University of Cambridge https://simons.berkeley.edu/talks/anuj-dawar-2016-08-29 Logical Structures in Computation Boot Camp
This is the third of six webinars provided by the Social Research Unit's intervention support team as part of the Realising Ambition project. The subject is 'Developing a Logic Model'. The issues covered are: - What is a logic model? - Why are logic models important? - What are the limitations of logic models? - How can logic models be developed and presented? - How do you make sure your logic model is logical? - How can you build an evidence base to support your logic model? http://www.dartington.org.uk/realisingambition
Subject : Economic Paper :Theory of Public Finance
Here we give the basic setup for Model Theory. I learned this from a talk Tom Scanlon gave in 2010 at CUNY.