Determinacy | Axioms of set theory | Large cardinals

Axiom of determinacy

In mathematics, the axiom of determinacy (abbreviated as AD) is a possible axiom for set theory introduced by Jan Mycielski and Hugo Steinhaus in 1962. It refers to certain two-person topological games of length ω. AD states that every game of a certain type is determined; that is, one of the two players has a winning strategy. Steinhaus and Mycielski's motivation for AD was its interesting consequences, and suggested that AD could be true in the smallest natural model L(R) of a set theory, which accepts only a weak form of the axiom of choice (AC) but contains all real and all ordinal numbers. Some consequences of AD followed from theorems proved earlier by Stefan Banach and Stanisław Mazur, and . Mycielski and Stanisław Świerczkowski contributed another one: AD implies that all sets of real numbers are Lebesgue measurable. Later Donald A. Martin and others proved more important consequences, especially in descriptive set theory. In 1988, John R. Steel and W. Hugh Woodin concluded a long line of research. Assuming the existence of some uncountable cardinal numbers analogous to , they proved the original conjecture of Mycielski and Steinhaus that AD is true in L(R). (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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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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9H The Determinant

Equivalent statements about the determinant.

From playlist Linear Algebra

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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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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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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

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From playlist Distinguished Visitors Lecture Series

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From playlist Oxford Mathematics Student Lectures - Set Theory

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9F The Determinant

Equivalent statements about the determinant.

From playlist Linear Algebra

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

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the notation of and how to calculated a determinant. (Part 2) Next video in this series can be seen at: https://youtu.be/k3ZmxI267Zo

From playlist LINEAR ALGEBRA 2: DETERMINANTS

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

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From playlist Franke Lectures in the Humanities

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9G The Determinant

Equaivalent statements about the determinant. Evaluating elementary matrices.

From playlist Linear Algebra

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9C The Determinant

More on properties of determinant.

From playlist Linear Algebra

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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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Properties of Determinants 1

This video explains how to find the value of determinants using determinant properties.

From playlist The Determinant of a Matrix

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Lec 15 | MIT 6.172 Performance Engineering of Software Systems, Fall 2010

Lecture 15: Nondeterministic Programming Instructor: Charles Leiserson View the complete course: http://ocw.mit.edu/6-172F10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 6.172 Performance Engineering of Software Systems

Related pages

Axiom of real determinacy | Set theory | Infinitary logic | Measurable cardinal | Clopen set | Topological game | Borel determinacy theorem | Woodin cardinal | Transfinite induction | Cardinality of the continuum | Banach–Mazur game | Stanisław Mazur | Ordinal number | Stefan Banach | Descriptive set theory | Borel set | Large cardinal | Natural number | Cardinal number | Mathematics | Real number | Inaccessible cardinal | Axiom of determinacy | Baire space (set theory) | L(R) | Property of Baire | Axiom | Cardinality | Martin measure | Hugo Steinhaus | Closed set