In mathematics, an unfoldable cardinal is a certain kind of large cardinal number. Formally, a cardinal number κ is λ-unfoldable if and only if for every transitive model M of cardinality κ of ZFC-minus-power set such that κ is in M and M contains all its sequences of length less than κ, there is a non-trivial elementary embedding j of M into a transitive model with the critical point of j being κ and j(κ) ≥ λ. A cardinal is unfoldable if and only if it is an λ-unfoldable for all ordinals λ. A cardinal number κ is strongly λ-unfoldable if and only if for every transitive model M of cardinality κ of ZFC-minus-power set such that κ is in M and M contains all its sequences of length less than κ, there is a non-trivial elementary embedding j of M into a transitive model "N" with the critical point of j being κ, j(κ) ≥ λ, and V(λ) is a subset of N. Without loss of generality, we can demand also that N contains all its sequences of length λ. Likewise, a cardinal is strongly unfoldable if and only if it is strongly λ-unfoldable for all λ. These properties are essentially weaker versions of strong and supercompact cardinals, consistent with V = L. Many theorems related to these cardinals have generalizations to their unfoldable or strongly unfoldable counterparts. For example, the existence of a strongly unfoldable implies the consistency of a slightly weaker version of the proper forcing axiom. A Ramsey cardinal is unfoldable, and will be strongly unfoldable in L. It may fail to be strongly unfoldable in V, however. In L, any unfoldable cardinal is strongly unfoldable; thus unfoldables and strongly unfoldables have the same consistency strength. A cardinal k is κ-strongly unfoldable, and κ-unfoldable, if and only if it is weakly compact. A κ+ω-unfoldable cardinal is totally indescribable and preceded by a stationary set of totally indescribable cardinals. (Wikipedia).
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From playlist Science Unplugged: Physics
In E=MC², what is c and what is its role?
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From playlist Science Unplugged: Special Relativity
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👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
Harald Helfgott - 2/4 Growth in groups and applications
Harald Helfgott - Growth in groups and applications
From playlist École d'été 2014 - Théorie analytique des nombres
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From playlist Doodling in Math and more | Math for fun and glory | Khan Academy
Hugo Duminil-Copin - 1/4 The Self-Avoiding Walk Model
The course will focus on rigorous results for the self-avoiding walk model on lattices, with a special emphasis on low-dimensional ones. The model is defined by choosing uniformly at random among random walk paths starting from the origin and without self-intersections. Despite its simple
From playlist Hugo Duminil-Copin - The Self-Avoiding Walk Model
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From playlist Science Unplugged: Parallel Universes
What are four types of polygons
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From playlist Classify Polygons
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Talk by Raphaël Beuzart-Plessis (Université d’Aix-Marseille,France)
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From playlist Seminars: Representation Theory and Number Theory
Assaf Rinot : Distributive Aronszajn trees
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From playlist Logic and Foundations
Does E=MC² manifest itself in everyday life?
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From playlist Science Unplugged: Special Relativity
What are the Angle Relationships for Parallel Lines and a Transversal
👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
MIT 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Fall 2012 View the complete course: http://ocw.mit.edu/6-849F12 Instructor: Erik Demaine This class covers creases in context of smoothness and a proof from the lecture involving Taylor expansion. Algorithms for the num
From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012
Join a physicist, a neuroscientist, and a linguist as they explore the deep enigmas of time. Time feels like it flows, but does it? Time seems to have a built-in direction, from past to future, but is that real or merely a quality imposed by the human brain? Time on earth elapses at a unif
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Bernard Muir, "Stanford Athletics: Setting an Example in a Changing Landscape"
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From playlist STANFORD+CONNECTS
Summation formulae and speculations on period integrals attached to triples... - Jayce Getz
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From playlist Mathematics
Proving Parallel Lines with Angle Relationships
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Nonetheless one should learn the language of topos: Grothendieck... - Colin McLarty [2018]
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From playlist Number Theory
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From playlist Science Unplugged: Physics