Mathematical logic | Set theory | Ordinal numbers | Proof theory

Theories of iterated inductive definitions

In set theory and logic, Buchholz's ID hierarchy is a hierarchy of subsystems of first-order arithmetic. The systems/theories are referred to as "the formal theories of ν-times iterated inductive definitions". IDν extends PA by ν iterated least fixed points of monotone operators. (Wikipedia).

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Inductive Reasoning

http://mathispower4u.wordpress.com/

From playlist Introduction to Proof

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Comparing Iterative and Recursive Factorial Functions

Comparing iterative and recursive factorial functions

From playlist Computer Science

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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

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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

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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

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Introducing Infinity | Set Theory, Section 3.1

In this video we define inductive sets, the natural numbers, the axiom of infinity, and the standard order relation on the natural numbers. My Twitter: https://twitter.com/KristapsBalodi3 Intro (0:00) Defining Natural Numbers as Sets (1:19) Definition of Inductive Sets (5:07) The Axiom o

From playlist Axiomatic Set Theory

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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

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Set Theory (Part 7): Natural Numbers and Induction

Please feel free to leave comments/questions on the video and practice problems below! In this video, I discuss the von Neumann construction of the natural numbers and relate the idea of natural numbers to inductive sets. The axiom of infinity is also introduced here as one of the ZFC axi

From playlist Set Theory by Mathoma

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Syntax and Semantics - Benedikt Ahrens

Benedikt Ahrens Universite Nice Sophia Antipolis; Member, School of Mathematics September 25, 2012 For more videos, visit http://video.ias.edu

From playlist Mathematics

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Axioms of Constructive Set Theory Explained

In this video we're going to discuss the various axiom schemes of constructive set theories and how they relate to type theory. I cover BCST, ECST, IKP, KPI, KP, CST, CZF, IZF, Mac Lane, Z and variants equi-consistent to ETCS from category theory, and then of course ZF and ZFC. The text I

From playlist Logic

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Dynamics of piecewise smooth maps (Lecture - 02) by Paul Glendinning

PROGRAM DYNAMICS OF COMPLEX SYSTEMS 2018 ORGANIZERS Amit Apte, Soumitro Banerjee, Pranay Goel, Partha Guha, Neelima Gupte, Govindan Rangarajan and Somdatta Sinha DATE: 16 June 2018 to 30 June 2018 VENUE: Ramanujan hall for Summer School held from 16 - 25 June, 2018; Madhava hall for W

From playlist Dynamics of Complex systems 2018

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Introduction to Witt Vectors, delta-rings,and prisms (Lecture - 3) by James Broger

PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath

From playlist Perfectoid Spaces 2019

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Kenji Fukaya: Inductive limit which appears in Lagrangian Floer theory

CIRM VIRTUAL EVENT Recorded during the meeting "From Hamiltonian Dynamics to Symplectic Topology" the April 26, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematic

From playlist Virtual Conference

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Type Systems - Vladimir Voevodsky

Vladimir Voevodsky Professor, School of Mathematics, IAS October 3, 2012 For more videos, visit http://video.ias.edu

From playlist Mathematics

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Injective, Surjective and Bijective Functions (continued)

This video is the second part of an introduction to the basic concepts of functions. It looks at the different ways of representing injective, surjective and bijective functions. Along the way I describe a neat way to arrive at the graphical representation of a function.

From playlist Foundational Math

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Corinna Ulcigrai - 3/4 Chaotic Properties of Area Preserving Flows

Flows on surfaces are one of the fundamental examples of dynamical systems, studied since Poincaré; area preserving flows arise from many physical and mathematical examples, such as the Novikov model of electrons in a metal, unfolding of billiards in polygons, pseudo-periodic topology. In

From playlist Corinna Ulcigrai - Chaotic Properties of Area Preserving Flows

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Overview of Univalent Foundations - Vladimir Voevodsky

Vladimir Voevodsky Institute for Advanced Study September 27, 2012 (Continued from September 26, 2012) For more videos, visit http://video.ias.edu

From playlist Mathematics

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Robin Deeley: The K-theory of the stable algebra and stable Ruelle algebra of a Wieler solenoid

Talk by Robin Deeley in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on May 13, 2020.

From playlist Global Noncommutative Geometry Seminar (Americas)

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How to Prove a Function is Injective(one-to-one) Using the Definition

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys How to prove a function is injective. Injective functions are also called one-to-one functions. This is a short video focusing on the proof.

From playlist Proofs

Related pages

Bachmann–Howard ordinal | Set theory | Mathematical logic | Second-order arithmetic | Peano axioms | Takeuti–Feferman–Buchholz ordinal