Determinacy | Axioms of set theory

Axiom of real determinacy

In mathematics, the axiom of real determinacy (abbreviated as ADR) is an axiom in set theory. It states the following: Axiom — Consider infinite two-person games with perfect information. Then, every game of length ω where both players choose real numbers is determined, i.e., one of the two players has a winning strategy. The axiom of real determinacy is a stronger version of the axiom of determinacy (AD), which makes the same statement about games where both players choose integers; ADR is inconsistent with the axiom of choice. It also implies the existence of inner models with certain large cardinals. ADR is equivalent to AD plus the axiom of uniformization. (Wikipedia).

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Ex: Determinant of a 2x2 Matrix

This video provides two examples of calculating a 2x2 determinant. One example contains fractions. Site: http://mathispower4u.com

From playlist The Determinant of a Matrix

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Gabriel Goldberg: The Jackson analysis and the strongest hypotheses

HYBRID EVENT Recorded during the meeting "XVI International Luminy Workshop in Set Theory" the September 13, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematician

From playlist Logic and Foundations

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Joel David Hamkins : The hierarchy of second-order set theories between GBC and KM and beyond

Abstract: Recent work has clarified how various natural second-order set-theoretic principles, such as those concerned with class forcing or with proper class games, fit into a new robust hierarchy of second-order set theories between Gödel-Bernays GBC set theory and Kelley-Morse KM set th

From playlist Logic and Foundations

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Linear Algebra: Ch 2 - Determinants (1 of 48) What is a Determinant? (Part 1)

Visit http://ilectureonline.com for more math and science lectures! In this video I will give a general definition of “What is a Determinant?” (Part 1) Next video in this series can be seen at: https://youtu.be/vIHnlNjRnGU

From playlist LINEAR ALGEBRA 2: DETERMINANTS

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Counting Woodin cardinals in HOD

Distinguished Visitor Lecture Series Counting Woodin cardinals in HOD W. Hugh Woodin Harvard University, USA and University of California, Berkeley, USA

From playlist Distinguished Visitors Lecture Series

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Finding randomness

Distinguished Visitor Lecture Series Finding randomness Theodore A. Slaman University of California, Berkeley, USA

From playlist Distinguished Visitors Lecture Series

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9F The Determinant

Equivalent statements about the determinant.

From playlist Linear Algebra

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Set Theory - What is Set Theory and what is it for? Oxford Mathematics 3rd Year Student Lecture

This is the first of four lectures from Robin Knight's 3rd Year Set Theory course. Robin writes: "Infinity baffled mathematicians, and everyone else, for thousands of years. But around 1870, Georg Cantor worked out how to study infinity in a way that made sense, and created set theory. Mo

From playlist Oxford Mathematics Student Lectures - Set Theory

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(3.2.3) The Determinant of Square Matrices and Properties

This video defines the determinant of a matrix and explains what a determinant means in terms of mapping and area. https://mathispower4u.com

From playlist Differential Equations: Complete Set of Course Videos

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9H The Determinant

Equivalent statements about the determinant.

From playlist Linear Algebra

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What is a real number?

Ordered Fields In this video, I define the notion of an order (or inequality) and then define the concept of an ordered field, and use this to give a definition of R using axioms. Actual Construction of R (with cuts): https://youtu.be/ZWRnZhYv0G0 COOL Construction of R (with sequences)

From playlist Real Numbers

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Determinant of an Operator and of a Matrix

Determinant of an operator. An operator is not invertible if and only if its determinant equals 0. Formula for the characteristic polynomial in terms of determinants. Determinant of a matrix. Connection between the two notions of determinant.

From playlist Linear Algebra Done Right

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Robert Pippin - Radical Finitude in the Anti-Idealist Modern European Philosophical Tradition”

Robert Pippin is Evelyn Stefansson Nef Distinguished Service Professor in the Committee on Social Thought, the Department of Philosophy, and the College at the University of Chicago. He is the author of Kant’s Theory of Form; Hegel’s Idealism: The Satisfactions of Self-Consciousness; Moder

From playlist Franke Lectures in the Humanities

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N and Order | Axiomatic Set Theory, Section 3.2

We prove the natural ordering on the natural numbers is a total order. Transitivity (0:00) Asymmetry (6:02) All elements are comparable (8:45)

From playlist Axiomatic Set Theory

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MM++ implies (*)

Ralf Schindler Universität Münster, Germany

From playlist Talks of Mathematics Münster's reseachers

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Characterization of the determinant

In this video, I show why the determinant is so special in math: Namely, it is the only function which is multilinear, alternating, and has the value 1 at the identity matrix. This is a generalization of a previous matrix puzzle for the 2 x 2 case. 2 x 2 case: https://youtu.be/lIMeIC1ZJO8

From playlist Determinants

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16. Nondeterministic Parallel Programming

MIT 6.172 Performance Engineering of Software Systems, Fall 2018 Instructor: Charles Leiserson View the complete course: https://ocw.mit.edu/6-172F18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63VIBQVWguXxZZi0566y7Wf Prof. Leiserson discusses nondeterministic paral

From playlist MIT 6.172 Performance Engineering of Software Systems, Fall 2018

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Difficulties with real numbers as infinite decimals ( I) | Real numbers + limits Math Foundations 91

There are three quite different approaches to the idea of a real number as an infinite decimal. In this lecture we look carefully at the first and most popular idea: that an infinite decimal can be defined in terms of an infinite sequence of digits appearing to the right of a decimal point

From playlist Math Foundations

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A new basis theorem for ∑13 sets

Distinguished Visitor Lecture Series A new basis theorem for ∑13 sets W. Hugh Woodin Harvard University, USA and University of California, Berkeley, USA

From playlist Distinguished Visitors Lecture Series

Related pages

Determinacy | Topological game | Large cardinal | Axiom | Axiom of projective determinacy | Set theory | Mathematics | Integer | Real number | Perfect information | Consistency | Ordinal number | Axiom of determinacy | AD+ | Inner model