In set theory, an ordinal number α is an admissible ordinal if Lα is an admissible set (that is, a transitive model of Kripke–Platek set theory); in other words, α is admissible when α is a limit ordinal and Lα ⊧ Σ0-collection. The term was coined by Richard Platek in 1966. The first two admissible ordinals are ω and (the least non-recursive ordinal, also called the Church–Kleene ordinal). Any regular uncountable cardinal is an admissible ordinal. By a theorem of Sacks, the countable admissible ordinals are exactly those constructed in a manner similar to the Church–Kleene ordinal, but for Turing machines with oracles. One sometimes writes for the -th ordinal that is either admissible or a limit of admissibles; an ordinal that is both is called recursively inaccessible. There exists a theory of large ordinals in this manner that is highly parallel to that of (small) large cardinals (one can define recursively Mahlo ordinals, for example). But all these ordinals are still countable. Therefore, admissible ordinals seem to be the recursive analogue of regular cardinal numbers. Notice that α is an admissible ordinal if and only if α is a limit ordinal and there does not exist a γ < α for which there is a Σ1(Lα) mapping from γ onto α. If M is a standard model of KP, then the set of ordinals in M is an admissible ordinal. (Wikipedia).
Definition of admissible and inadmissible estimators.
From playlist Machine Learning
What is an Injective Function? Definition and Explanation
An explanation to help understand what it means for a function to be injective, also known as one-to-one. The definition of an injection leads us to some important properties of injective functions! Subscribe to see more new math videos! Music: OcularNebula - The Lopez
From playlist Functions
Abstract Algebra | Injective Functions
We give the definition of an injective function, an outline of proving that a given function is injective, and a few examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
The idea of ‘atonement’ sounds very old-fashioned and is deeply rooted in religious tradition. To atone means, in essence, to acknowledge one’s capacity for wrongness and one’s readiness for apology and desire for change. It’s a concept that every society needs at its center. For gifts and
From playlist RELATIONSHIPS
ADVERBS OF DEGREE - ENGLISH GRAMMAR
Adverbs of degree are words that describe or modify adjectives or adverbs. They are a special type of adverb, so I don't really like to think of them as adverbs. They are best on their own category. These are also called intensifiers or qualifiers. If you want to support the channel, hit
From playlist English Grammar
Definition of a Surjective Function and a Function that is NOT Surjective
We define what it means for a function to be surjective and explain the intuition behind the definition. We then do an example where we show a function is not surjective. Surjective functions are also called onto functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear ht
From playlist Injective, Surjective, and Bijective Functions
A new basis theorem for ∑13 sets
Distinguished Visitor Lecture Series A new basis theorem for ∑13 sets W. Hugh Woodin Harvard University, USA and University of California, Berkeley, USA
From playlist Distinguished Visitors Lecture Series
We show the connection between the method of adjoints in optimal control to the implicit function theorem ansatz. We relate the costate or adjoint state variable to Lagrange multipliers.
From playlist There and Back Again: A Tale of Slopes and Expectations (NeurIPS-2020 Tutorial)
Counting Woodin cardinals in HOD
Distinguished Visitor Lecture Series Counting Woodin cardinals in HOD W. Hugh Woodin Harvard University, USA and University of California, Berkeley, USA
From playlist Distinguished Visitors Lecture Series
Definition of an Injective Function and Sample Proof
We define what it means for a function to be injective and do a simple proof where we show a specific function is injective. Injective functions are also called one-to-one functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear https://amzn.to/3BFvcxp (these are my affil
From playlist Injective, Surjective, and Bijective Functions
David Natingga: Towards Embedding Theorem: Aut(Dαe) embeds into Aut(Dα)
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: The researchers Cai, Ganchev, Lempp, Miller and Soskova proved that the total Turing degrees TOTe are definable in the enumeration degrees De: a degree is total iff it i
From playlist Workshop: "Proof, Computation, Complexity"
The Toledo War: When Ohio and Michigan Went to War and Wisconsin Lost
In 1835, a dispute based on a faulty map brought the State of Ohio and the Michigan Territory to the brink of war. The "Toledo War" represented the stresses of a growing nation, and rewrote the boundaries of three states. It is history that deserves to be remembered. This is original con
From playlist US History
Measures of Location, Mean, Median, Mode and Central Tendency in Business Statistics (Week 5A)
Three measures of central tendency (i.e. location) tell us mean, median, and mode of data. We choose our measure of location based on the level of the data, such as the mode for nominal, median for ordinal, and mean for scale variables. We may change our measure of location based on the ch
From playlist Basic Business Statistics (QBA 237 - Missouri State University)
Moving the US to a war footing before and during the Second World War was probably the largest industrial shift in American history. In rural Wisconsin, the largest munition factory in the world sprung up as if out of nowhere, just one of many military facilities the size of cities built
From playlist US History
Simple Measures of Variability: PERCENTILES, Quartiles, & Range (5-8)
Variability is about how close together or spread out the scores are. The simplest measures of variability consider all of the data and divide it into smaller chunks like tenths, hundredths, or quarters. Chapters 0:00 simple measurements of variability 0:28 Percentiles 1:34 Quartiles 2:0
From playlist Central Tendency and Variability in Statistics (WK 5 - QBA 237)
Graph Data Structure 6. The A* Pathfinding Algorithm
This is the sixth in a series of videos about the graph data structure. It includes a step by step walkthrough of the A* pathfinding algorithm (pronounced A Star) for a weighted, undirected graph. The A* pathfinding algorithm, and its numerous variations, is widely used in applications suc
From playlist Path Finding Algorithms
Direct substitution with the left hand limit
👉 Learn how to evaluate the limit of a function involving rational expressions. The limit of a function as the input variable of the function tends to a number/value is the number/value which the function approaches at that time. The limit of a function is usually evaluated by direct subst
From playlist Evaluate the Limit (PC)
Measures of Variability, Variance, Standard Deviation, & Dispersion in Business Statistics (Week 5B)
We explore measures of variability such as range, interquartile range, variance, standard deviation, percentiles and quartiles. We explore how to create variance by squaring deviation scores then set it all right again with the standard deviation. Dr. Daniel shows you how to create measure
From playlist Basic Business Statistics (QBA 237 - Missouri State University)
Research at the Interface of Computer Science and Economics by Swaprava Nath
Program Summer Research Program on Dynamics of Complex Systems ORGANIZERS: Amit Apte, Soumitro Banerjee, Pranay Goel, Partha Guha, Neelima Gupte, Govindan Rangarajan and Somdatta Sinha DATE : 15 May 2019 to 12 July 2019 VENUE : Madhava hall for Summer School & Ramanujan hall f
From playlist Summer Research Program On Dynamics Of Complex Systems 2019
Evaluate the left hand limit at an asymptote algebraically
👉 Learn how to evaluate the limit of a function involving rational expressions. The limit of a function as the input variable of the function tends to a number/value is the number/value which the function approaches at that time. The limit of a function is usually evaluated by direct subst
From playlist Evaluate the Limit (PC)