Descriptive set theory | Determinacy | Axioms of set theory | Game theory | Large cardinals

Axiom of projective determinacy

In mathematical logic, projective determinacy is the special case of the axiom of determinacy applying only to projective sets. The axiom of projective determinacy, abbreviated PD, states that for any two-player infinite game of perfect information of length ω in which the players play natural numbers, if the victory set (for either player, since the projective sets are closed under complementation) is projective, then one player or the other has a winning strategy. The axiom is not a theorem of ZFC (assuming ZFC is consistent), but unlike the full axiom of determinacy (AD), which contradicts the axiom of choice, it is not known to be inconsistent with ZFC. PD follows from certain large cardinal axioms, such as the existence of infinitely many Woodin cardinals. PD implies that all projective sets are Lebesgue measurable (in fact, universally measurable) and have the perfect set property and the property of Baire. It also implies that every projective binary relation may be uniformized by a projective set. (Wikipedia).

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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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9H The Determinant

Equivalent statements about the determinant.

From playlist Linear Algebra

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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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Gabriel Goldberg: The Jackson analysis and the strongest hypotheses

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From playlist Logic and Foundations

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Counting Woodin cardinals in HOD

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From playlist Logic and Foundations

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(3.2.3) The Determinant of Square Matrices and Properties

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From playlist Differential Equations: Complete Set of Course Videos

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9F The Determinant

Equivalent statements about the determinant.

From playlist Linear Algebra

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From playlist Distinguished Visitors Lecture Series

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MM++ implies (*)

Ralf Schindler Universität Münster, Germany

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9G The Determinant

Equaivalent statements about the determinant. Evaluating elementary matrices.

From playlist Linear Algebra

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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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From playlist Linear Algebra Lectures

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9C The Determinant

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From playlist Linear Algebra

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16. Nondeterministic Parallel Programming

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

Related pages

Binary relation | Large cardinal | Property of Baire | Mathematical logic | Perfect set property | Natural number | Woodin cardinal | Uniformization (set theory) | Perfect information | Axiom of determinacy