Independence results | Trees (set theory)
In set theory, a Kurepa tree is a tree (T, <) of height ω1, each of whose levels is at most countable, and has at least ℵ2 many branches. This concept was introduced by Kurepa. The existence of a Kurepa tree (known as the Kurepa hypothesis, though Kurepa originally conjectured that this was false) is consistent with the axioms of ZFC: Solovay showed in unpublished work that there are Kurepa trees in Gödel's constructible universe. More precisely, the existence of Kurepa trees follows from the diamond plus principle, which holds in the constructible universe. On the other hand, Silver showed that if a strongly inaccessible cardinal is Lévy collapsed to ω2 then, in the resulting model, there are no Kurepa trees. The existence of an inaccessible cardinal is in fact equiconsistent with the failure of the Kurepa hypothesis, because if the Kurepa hypothesis is false then the cardinal ω2 is inaccessible in the constructible universe. A Kurepa tree with fewer than 2ℵ1 branches is known as a Jech–Kunen tree. More generally if κ is an infinite cardinal, then a κ-Kurepa tree is a tree of height κ with more than κ branches but at most |α| elements of each infinite level α<κ, and the Kurepa hypothesis for κ is the statement that there is a κ-Kurepa tree. Sometimes the tree is also assumed to be binary. The existence of a binary κ-Kurepa tree is equivalent to the existence of a Kurepa family: a set of more than κ subsets of κ such that their intersections with any infinite ordinal α<κ form a set of cardinality at most α. The Kurepa hypothesis is false if κ is an ineffable cardinal, and conversely Jensen showed that in the constructible universe for any uncountable regular cardinal κ there is a κ-Kurepa tree unless κ is ineffable. (Wikipedia).
Greening of Bangalore by Vijay Thiruvady
KAAPI WITH KURIOSITY GREENING OF BANGALORE SPEAKER: Vijay Thiruvady (Bangalore Environment Trust) WHEN: 4:00 pm to 5:30 pm Sunday, 26 June 2022 WHERE: Jawaharlal Nehru Planetarium, Bengaluru Abstract: The oldest extant greenery is found in the Nallur Amaroy Thopu which is a Devara
From playlist Kaapi With Kuriosity (A Monthly Public Lecture Series)
Mirna Džamonja: Universal א2-Aronszajn trees
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From playlist Logic and Foundations
#Mandala MANDALA LOVERS ALERT- Mandala (Sanskrit: मण्डल, lit, circle) is a spiritual and ritual symbol in Indian religions, representing the universe-check out more videos about mandala below-. * check out my Blog Post for details on Mandala supplies- https://www.theartgeekblog.com/post/mu
From playlist Bag
Engineering Wall Clock! https://teespring.com/flammable-math-clock Support the channel by signing up on Brilliant for FREE using the link https://brilliant.org/FlammableMaths ! =D Gamma Fct: https://youtu.be/0170T5uyfuM Today we take a look at the sum of factorials k! :) This interestin
From playlist Integrals
Finally moving on to dynamic huffman trees, sort of... -- Watch live at https://www.twitch.tv/simuleios
From playlist Huffman forest
Well, we got the first iteration of the tree drawn, but it doesn't look quite right... -- Watch live at https://www.twitch.tv/simuleios
From playlist Huffman forest
Cucumber Chutney - By VahChef @ VahRehVah.com
Dosakaya Pachadi is an easy to make Indian food recipe. A traditional Andhra pachadi where lemon cucumber is crushed with roasted lentils Cucumber or the lemon cucumber is also called as Dosakaya in Telugu is a cherished vegetable in Andhra cuisine. This exotic chutney is prepared by addin
From playlist Cusine
37 Tallest Statues in the World Height and Size Comparison 3D
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From playlist Comparison
The World's Tallest Tree! | Science for Kids
Can you guess how tall the tallest tree is? Neither could we! Tag along with Jessi and Squeaks to learn all about the world’s tallest tree! ---------- Like SciShow? Want to help support us, and also get things to put on your walls, cover your torso and hold your liquids? Check out our awes
From playlist SciShow Kids
We look at the oak tree, and why our ecologist says it should lead to a new national holiday in the England. More at http://www.test-tube.org.uk/trees/
From playlist Guide to Trees & Plants
Tree Representation for XML, JSON and Symbolic Expressions: Live with the R&D team
Presentation begins at 0:53 In this stream, we have a Tree Representation for XML, JSON and Symbolic Expressions with Wolfram R&D. Follow us on our official social media channels. Twitter: https://twitter.com/WolframResearch/ Facebook: https://www.facebook.com/wolframresearch/ Ins
From playlist Live with the R&D Team
Trees are fundamental data structures in mathematics and science, with standard examples including XML trees, file systems and Wolfram Language expressions. We present symbolic Tree objects, added in Version 12.3 of the Wolfram Language, which are used to represent rooted, ordered, labeled
From playlist Wolfram Technology Conference 2021
Game Programming Patterns 8.2 - (JavaScript) Prototype pattern
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From playlist Game Programming Patterns Book
Game Programming Patterns part 8.3 - (Rust) Prototype Pattern
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From playlist Game Programming Patterns Book
Live CEOing Ep 548: Language Design in Wolfram Language [ExpressionTree & Expressions vs Trees]
In this episode of Live CEOing, Stephen Wolfram discusses upcoming improvements and features to the Wolfram Language. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or through the official Twitch channel of Stephen Wolfram
From playlist Behind the Scenes in Real-Life Software Design
Live CEOing Ep 428: Language Design in Wolfram Language [Trees]
In this episode of Live CEOing, Stephen Wolfram discusses upcoming improvements and functionality to the Wolfram Language. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or through the official Twitch channel of Stephen Wo
From playlist Behind the Scenes in Real-Life Software Design
New in Tree Data & Computation
Tree is a new fundamental construct in the Wolfram Language added in Version 12.3 used to represent rooted, ordered, labeled trees. In this talk, we will present a variety of new features added in Version 13.1, including support for associations between keys and children, new ways of const
From playlist Wolfram Technology Conference 2022
Today we made progress towards understanding dynamic huffman trees again. -- Watch live at https://www.twitch.tv/simuleios
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Reconstructing phylogenetic networks from trees by Simone Linz
CMSA Combinatorics Seminar, 27 October 2020
From playlist CMSA Combinatorics Seminar