In mathematics, a remarkable cardinal is a certain kind of large cardinal number. A cardinal κ is called remarkable if for all regular cardinals θ > κ, there exist π, M, λ, σ, N and ρ such that 1. * π : M → Hθ is an elementary embedding 2. * M is countable and transitive 3. * π(λ) = κ 4. * σ : M → N is an elementary embedding with critical point λ 5. * N is countable and transitive 6. * ρ = M ∩ Ord is a regular cardinal in N 7. * σ(λ) > ρ 8. * M = HρN, i.e., M ∈ N and N ⊨ "M is the set of all sets that are hereditarily smaller than ρ" Equivalently, is remarkable if and only if for every there is such that in some forcing extension , there is an elementary embedding satisfying . Although the definition is similar to one of the definitions of supercompact cardinals, the elementary embedding here only has to exist in , not in . (Wikipedia).
The Power of Notre Dame Cathedral: Professor William R. Cook
With its famous facade and its iconic status as one of the world's foremost cathedrals, Notre Dame has been remodeled more often than any other cathedral (most notably after the French Revolution). With an estimated length of 400 feet, the cathedral features an innovative double-aisled nav
From playlist Modern History
Michelangelo Explained: From Pietà to the Sistine Chapel
Why is Michelangelo so different from other artists in the Renaissance? He is considered such a genius not only for his masterly craftsmanship, but because of the way he conceived his pieces of art. Explore his works with me and understand his art. Subtitles available in several languages
From playlist Vídeos
Did Albert Einstein believe in God?
What made Albert Einstein one of the greatest scientific geniuses the world has ever known? His scientific breakthroughs revolutionized the way we understand the universe. The World Science Festival, in partnership with the 92Y’s 7 Days of Genius Festival, presents an in-depth look into th
From playlist The Life and Work of Albert Einstein
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From playlist Amazing Stuff
Isaac Newton - English Physicist & Formulated the Laws of Gravity |Mini Bio | BIO
Watch a short biography of Isaac Newton, a key figure in the scientific revolution who is most famous for formulating laws of gravity. #Biography Subscribe for more Biography: http://aetv.us/2AsWMPH Delve deeper into Biography on our site: http://www.biography.com Follow Biography for mo
From playlist Genius & Innovation | A+E Networks
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From playlist Science Unplugged: Special Relativity
Sumfree Sets (Lecture 1) by Jean-Marc Deshouillers
Program Workshop on Additive Combinatorics ORGANIZERS: S. D. Adhikari and D. S. Ramana DATE: 24 February 2020 to 06 March 2020 VENUE: Madhava Lecture Hall, ICTS Bangalore Additive combinatorics is an active branch of mathematics that interfaces with combinatorics, number theory, ergod
From playlist Workshop on Additive Combinatorics 2020
R. Dujardin - Some problems of arithmetic origin in complex dynamics and geometry (part3)
Some themes inspired from number theory have been playing an important role in holomorphic and algebraic dynamics (iteration of rational mappings) in the past ten years. In these lectures I would like to present a few recent results in this direction. This should include: the dynamica
From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes
The Nightingale and the Rose by Oscar Wilde - Audiobook read by John Gielgud
The Nightingale and the Rose by Oscar Wilde read by Sir John Gielgud
From playlist Old Audiobooks
Stanford: Pursuing the Next Great Discovery
Since Stanford first opened its doors to students and faculty, a core tenet of the university has been for its citizens to improve the world around them. Stanford researchers have achieved this goal repeatedly over the years, through the development of devices that made radar and MRI scans
From playlist Stanford Highlights
Today we delve into the history of this dynamic monument, which is the most impressive building that the Romans ever built, and perhaps the most influential building in the history of architecture. Like and subscribe to see more videos like this. Mira el vídeo en español: https://youtu.be
From playlist Vídeos
Nonlinear algebra, Lecture 13: "Polytopes and Matroids ", by Mateusz Michalek
This is the thirteenth lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
Fundamentals of Mathematics - Lecture 32.2 : Proof of the Pidgeonhole Principle
https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html
From playlist Fundamentals of Mathematics
Philosophy of Mathematics & Frege (Dummett 1994)
Michael Dummett gives a talk on Frege and the philosophy of mathematics. For a good introduction to the philosophy of mathematics, check out: https://www.youtube.com/watch?v=UhX1ouUjDHE Another good introduction to the philosophy of mathematics: https://www.youtube.com/watch?v=XyXWnGFKTkg
From playlist Logic & Philosophy of Mathematics
The Green - Tao Theorem (Lecture 3) by D. S. Ramana
Program Workshop on Additive Combinatorics ORGANIZERS: S. D. Adhikari and D. S. Ramana DATE: 24 February 2020 to 06 March 2020 VENUE: Madhava Lecture Hall, ICTS Bangalore Additive combinatorics is an active branch of mathematics that interfaces with combinatorics, number theory, ergod
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A road to the infinities: Some topics in set theory by Sujata Ghosh
PROGRAM : SUMMER SCHOOL FOR WOMEN IN MATHEMATICS AND STATISTICS ORGANIZERS : Siva Athreya and Anita Naolekar DATE : 13 May 2019 to 24 May 2019 VENUE : Ramanujan Lecture Hall, ICTS Bangalore The summer school is intended for women students studying in first year B.A/B.Sc./B.E./B.Tech.
From playlist Summer School for Women in Mathematics and Statistics 2019
History and Science of Ancient Astronomy - Stonehenge and Archaeoastronomy
Learn more about this course and sign up for a FREE trial of The Great Courses Plus here: https://wondrium.com/youtube/lp/t2/generic?utm_source=Video&utm_medium=Youtube&utm_campaign=149636 Ancient people viewed the sky differently than we do. Skywatching was crucial to the ancients’ daily
From playlist Science
Richard Dawkins & Lawrence Krauss: Something from Nothing
Critically-acclaimed author and evolutionary biologist Richard Dawkins and world-renowned theoretical physicist and author Lawrence Krauss discuss biology, cosmology, religion, and a host of other topics at this event entitled 'Something from Nothing'. This video was recorded at The Austr
From playlist Richard Dawkins
Lec 14 | MIT 6.046J / 18.410J Introduction to Algorithms (SMA 5503), Fall 2005
Lecture 14: Competitive Analysis: Self-organizing Lists View the complete course at: http://ocw.mit.edu/6-046JF05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.046J / 18.410J Introduction to Algorithms (SMA 5503),
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