In recursion theory, α recursion theory is a generalisation of recursion theory to subsets of admissible ordinals . An admissible set is closed under functions, where denotes a rank of Godel's constructible hierarchy. is an admissible ordinal if is a model of Kripke–Platek set theory. In what follows is considered to be fixed. The objects of study in recursion are subsets of . These sets are said to have some properties: * A set is said to be -recursively-enumerable if it is definable over , possibly with parameters from in the definition. * A is -recursive if both A and (its relative complement in ) are -recursively-enumerable. It's of note that -recursive sets are members of by definition of . * Members of are called -finite and play a similar role to the finite numbers in classical recursion theory. There are also some similar definitions for functions mapping to : * A function mapping to is -recursively-enumerable iff its graph is -definable in . * A function mapping to is -recursive iff its graph is -definable in . * Additionally, a function mapping to is -arithmetical iff there exists some such that the function's graph is -definable in . Additional connections between recursion theory and α recursion theory can be drawn, although explicit definitions may not have yet been written to formalize them: * The functions -definable in play a role similar to those of the primitive recursive functions. We say R is a reduction procedure if it is recursively enumerable and every member of R is of the form where H, J, K are all α-finite. A is said to be α-recursive in B if there exist reduction procedures such that: If A is recursive in B this is written . By this definition A is recursive in (the empty set) if and only if A is recursive. However A being recursive in B is not equivalent to A being . We say A is regular if or in other words if every initial portion of A is α-finite. (Wikipedia).
Applying the recursive formula to a sequence to determine the first five terms
👉 Learn all about recursive sequences. Recursive form is a way of expressing sequences apart from the explicit form. In the recursive form of defining sequences, each term of a sequence is expressed in terms of the preceding term unlike in the explicit form where each term is expressed in
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Using the recursive formula to find the first four terms of a sequence
👉 Learn all about recursive sequences. Recursive form is a way of expressing sequences apart from the explicit form. In the recursive form of defining sequences, each term of a sequence is expressed in terms of the preceding term unlike in the explicit form where each term is expressed in
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Set Theory (Part 10): Natural Number Arithmetic
Please feel free to leave comments/questions on the video and practice problems below! In this video, we utilize the recursion theorem to give a theoretical account of arithmetic on the natural numbers. We will also see that the common properties of addition, multiplication, etc. are now
From playlist Set Theory by Mathoma
Compare Linear and Exponential Growth Using Recursive and Explicit Equations
This video explains the different between linear and exponential growth. Both recursive and explicit equations are discussed. Site: http://mathispower4u.com
From playlist Linear, Exponential, and Logistic Growth: Recursive/Explicit
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
Bertrand Eynard - Considerations about Resurgence Properties of Topological Recursion
To a spectral curve $S$ (e.g. a plane curve with some extra structure), topological recursion associates a sequence of invariants: some numbers $F_g(S)$ and some $n$-forms $W_{g,n}(S)$. First we show that $F_g(S)$ grow at most factorially at large $g$, $F_g = O((
From playlist Resurgence in Mathematics and Physics
How to use the recursive formula to evaluate the first five terms
👉 Learn all about recursive sequences. Recursive form is a way of expressing sequences apart from the explicit form. In the recursive form of defining sequences, each term of a sequence is expressed in terms of the preceding term unlike in the explicit form where each term is expressed in
From playlist Sequences
How to determine the first five terms for a recursive sequence
👉 Learn all about recursive sequences. Recursive form is a way of expressing sequences apart from the explicit form. In the recursive form of defining sequences, each term of a sequence is expressed in terms of the preceding term unlike in the explicit form where each term is expressed in
From playlist Sequences
Learn how to find the first five terms of a sequence using the recursive formula
👉 Learn all about recursive sequences. Recursive form is a way of expressing sequences apart from the explicit form. In the recursive form of defining sequences, each term of a sequence is expressed in terms of the preceding term unlike in the explicit form where each term is expressed in
From playlist Sequences
Introduction to Amplitudes (Lecture 2) by Marcus Spradlin
RECENT DEVELOPMENTS IN S-MATRIX THEORY (ONLINE) ORGANIZERS: Alok Laddha, Song He and Yu-tin Huang DATE: 20 July 2020 to 31 July 2020 VENUE:Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through online lecture
From playlist Recent Developments in S-matrix Theory (Online)
Elba Garcia-Failde: Introduction to topological recursion - Lecture 3
Mini course of the conference "Noncommutative geometry meets topological recursion", August 2021, University of Münster. Abstract: In this mini-course I will introduce the universal procedure of topological recursion, both by treating examples and by presenting the general formalism. We wi
From playlist Noncommutative geometry meets topological recursion 2021
Danilo Lewanski : Orbifold Hurwitz numbers, topological recursion and ELSV-type formulae
Recording during the thematic meeting : "Pre-School on Combinatorics and Interactions" the January 13, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Combinatorics
Thomas KRAJEWSKI - Connes-Kreimer Hopf Algebras...
Connes-Kreimer Hopf Algebras : from Renormalisation to Tensor Models and Topological Recursion At the turn of the millenium, Connes and Kreimer introduced Hopf algebras of trees and graphs in the context of renormalisation. We will show how the latter can be used to formulate the analogu
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Joel David Hamkins : The hierarchy of second-order set theories between GBC and KM and beyond
Abstract: Recent work has clarified how various natural second-order set-theoretic principles, such as those concerned with class forcing or with proper class games, fit into a new robust hierarchy of second-order set theories between Gödel-Bernays GBC set theory and Kelley-Morse KM set th
From playlist Logic and Foundations
Applying the recursive formula to a geometric sequence
👉 Learn all about recursive sequences. Recursive form is a way of expressing sequences apart from the explicit form. In the recursive form of defining sequences, each term of a sequence is expressed in terms of the preceding term unlike in the explicit form where each term is expressed in
From playlist Sequences
A New Physics-Inspired Theory of Deep Learning | Optimal initialization of Neural Nets
A special video about recent exciting developments in mathematical deep learning! 🔥 Make sure to check out the video if you want a quick visual summary over contents of the “The principles of deep learning theory” book https://deeplearningtheory.com/. SPONSOR: Aleph Alpha 👉 https://app.al
From playlist Explained AI/ML in your Coffee Break
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For more information about Stanford's Artificial Intelligence professional and graduate programs visit: https://stanford.io/ai To follow along with the course, visit: https://web.stanford.edu/class/stats214/ To view all online courses and programs offered by Stanford, visit: http://onli
From playlist Stanford CS229M: Machine Learning Theory - Fall 2021
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Recursively defined sets are an important concept in mathematics, computer science, and other fields because they provide a framework for defining complex objects or structures in a simple, iterative way. By starting with a few basic objects and applying a set of rules repeatedly, we can g
From playlist All Things Recursive - with Math and CS Perspective
Distinguished Visitor Lecture Series Finding randomness Theodore A. Slaman University of California, Berkeley, USA
From playlist Distinguished Visitors Lecture Series