In set theory and computability theory, Kleene's is a canonical subset of the natural numbers when regarded as ordinal notations. It contains ordinal notations for every computable ordinal, that is, ordinals below Church–Kleene ordinal, . Since is the first ordinal not representable in a computable system of ordinal notations the elements of can be regarded as the canonical ordinal notations. Kleene (1938) described a system of notation for all computable ordinals (those less than the Church–Kleene ordinal). It uses a subset of the natural numbers instead of finite strings of symbols. Unfortunately, there is in general no effective way to tell whether some natural number represents an ordinal, or whether two numbers represent the same ordinal. However, one can effectively find notations which represent the ordinal sum, product, and power (see ordinal arithmetic) of any two given notations in Kleene's ; and given any notation for an ordinal, there is a computably enumerable set of notations which contains one element for each smaller ordinal and is effectively ordered. (Wikipedia).
Here's the first of a new series about Korean culture. Objects in everyday life that remind you that you are in Korea. Pease, give me your feedback about it! Find me on FaceBook: http://www.facebook.com/pages/YouTube-TyYanns-page/130204640380067
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Baby koalas eat their mom's poop... and that's just the beginning. Subscribe! http://bit.ly/1FkxVLb ‖ Twitter! https://twitter.com/gross_science ‖ Tumblr! http://grossscience.tumblr.com/ ↓Want more info?↓ Additional info about the koala life cycle: http://bit.ly/1HPTmW4 Info on the koala
From playlist Gross Science
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From playlist Medical Education
The Sexiest Vegetable | FoodStuff
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From playlist Stuff About Food
Paulo Oliva: On a Dialectica like version of Kleene numerical realizability
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: Kleene's original notion of realizability (1945) makes use of all (partial) computable functions as potential realisers. Later Kreisel (1959) presented a "modified" notio
From playlist Workshop: "Proofs and Computation"
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The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: Progressions of theories along paths through Kleene's $\mathcal O$, adding the consistency of the previous theory at every successor step, can deduce every true $\Pi^0_1$
From playlist Workshop: "Proof, Computation, Complexity"
From playlist CS124 - Full Course
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From playlist Philosophy & Psychology 🧠
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From playlist Toy Ind3
A single Krispy Kreme store can produce 100,000 doughnuts a day. To learn more about how these Krispy Kreme doughnuts are made, check out this episode of BrainStuff. Whether the topic is popcorn or particle physics, you can count on the HowStuffWorks team to explore - and explain - the ev
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Hugo Herbelin: Computing with Markov's principle
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Makoto Fujiwara: Bar theorem and bar recursion for continuous functions with continuous modulus
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From playlist Workshop: "Constructive Mathematics"
MathWorks Excellence in Innovation Project 208: RC Car Modelling and Trajectory Tracking Control
Github project repository : https://github.com/Arttrm/MW_EiI_208_Trajectory_Planning_and_Tracking MathWorks Excellence in Innovation Projects : https://github.com/mathworks/MathWorks-Excellence-in-Innovation
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Iosif Petrakis: Bishop spaces and the problem of constructivizing general topology
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From playlist What is math used for?