Formal theories of arithmetic

Robinson arithmetic

In mathematics, Robinson arithmetic is a finitely axiomatized fragment of first-order Peano arithmetic (PA), first set out by R. M. Robinson in 1950. It is usually denoted Q. Q is almost PA without the axiom schema of mathematical induction. Q is weaker than PA but it has the same language, and both theories are incomplete. Q is important and interesting because it is a finitely axiomatized fragment of PA that is recursively incompletable and essentially undecidable. (Wikipedia).

Video thumbnail

Using Clocks to Solve Fractions String 8

A fun string dealing with subtraction that leads to sixths and twelfths

From playlist Arithmetic and Pre-Algebra: Fractions, Decimals and Percents

Video thumbnail

Number theory Full Course [A to Z]

Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure #mathematics devoted primarily to the study of the integers and integer-valued functions. Number theorists study prime numbers as well as the properties of objects made out of integers (for example, ratio

From playlist Number Theory

Video thumbnail

Regularity and non-standard models of arithmetic #PaCE1

Follow-up video: https://youtu.be/7HKnOOvssvs Discussed text, including all links: https://gist.github.com/Nikolaj-K/101c2712dc832dec4991bf568869abc8 Curt's call: https://youtu.be/V93GQaDtv8w Timestamps: 00:00:00 Introduction 00:02:55 Wittgenstein and predicates (optional) 00:11:12 Skolems

From playlist Logic

Video thumbnail

Using Clocks to Solve Fractions String 4

More connections between clocks and fractions. Here we introduce 1/10

From playlist Arithmetic and Pre-Algebra: Fractions, Decimals and Percents

Video thumbnail

Review of arithmetic with decimals II | Year 9 Maths 5 | NJ Wildberger

We continue our review or arithmetic with decimal numbers. How do we multiply two decimal numbers? How do we divide one decimal number by another? The trick is to realize that by suitably multiplying and dividing by powers of 10, these problems essentially reduce to arithmetic with ordinar

From playlist Year9Maths

Video thumbnail

Abraham Robinson’s legacy in model theory and (...) - L. Van den Dries - Workshop 3 - CEB T1 2018

Lou Van den Dries (University of Illinois, Urbana) / 27.03.2018 Abraham Robinson’s legacy in model theory and its applications ---------------------------------- Vous pouvez nous rejoindre sur les réseaux sociaux pour suivre nos actualités. Facebook : https://www.facebook.com/InstitutHe

From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields

Video thumbnail

Finding randomness

Distinguished Visitor Lecture Series Finding randomness Theodore A. Slaman University of California, Berkeley, USA

From playlist Distinguished Visitors Lecture Series

Video thumbnail

Using Clocks to Solve Fractions String 6

Here we use the clock model to deal with 3/18 and 3/9

From playlist Arithmetic and Pre-Algebra: Fractions, Decimals and Percents

Video thumbnail

Using Clocks to Solve Fractions String 1

Using a clock model and the patterns in a fraction string to make sense of unfriendly fractions

From playlist Arithmetic and Pre-Algebra: Fractions, Decimals and Percents

Video thumbnail

Number Theory - Fundamental Theorem of Arithmetic

Fundamental Theorem of Arithmetic and Proof. Building Block of further mathematics. Very important theorem in number theory and mathematics.

From playlist Proofs

Video thumbnail

Turing: Pioneer of the Information Age

(May 2, 2012) Following a three minute introduction by Steven Ericsson-Zenith, Jack Copeland discusses Alan Turing's impact on information technology. Turing is often considered to be one of the greatest minds in the 20th century, and Copeland looks at how many of Turing's ideas lie behind

From playlist Engineering

Video thumbnail

Unentscheidbare Probleme in der Mathematik

Prof. Dr. Dr. Katrin Tent, Mathematikerin von der Universität Münster und derzeit Gastwissenschaftlerin am Hausdorff Research Institute for Mathematics (HIM) der Universität Bonn, sprach im 200. Jahr des Bestehens der Bonner Alma Mater über "Unterschjeidbare Probleme in der Mathematik":

From playlist Hausdorff Center goes public

Video thumbnail

Using Clocks to Solve Fractions String 2

Another introductory video using clocks to understand fractions

From playlist Arithmetic and Pre-Algebra: Fractions, Decimals and Percents

Video thumbnail

Live CEOing Ep 09: Representing Proofs in the Wolfram Language

Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Representing Proofs in the Wolfram Language.

From playlist Behind the Scenes in Real-Life Software Design

Video thumbnail

4 Synthetic A Priori Judgments - Kant's Critique of Pure Reason (Dan Robinson)

Dan Robinson gives the 4th lecture in a series of 8 on Immanuel Kant's Critique of Pure Reason. All 8 lectures: https://www.youtube.com/playlist?list=PLhP9EhPApKE_OdgqNgL0AJX9-gwr4tmLw Kant claims that, "our sense representation is not a representation of things in themselves, but of th

From playlist Kant's Critique of Pure Reason - Dan Robinson

Video thumbnail

😊🤔😔😁😕😮😍 in Maths - Vicky Neale

Oxford Mathematics Newcastle Public Lecture: Vicky Neale - 😊🤔😔😁😕😮😍 in Maths Mathematics has no place for emotion. Mathematicians are positively unemotional. True? Well, no. In fact 10 out of 10 untrue. Mathematics and mathematicians are also on the emotional rollercoaster. Vicky Neale te

From playlist A Vicky Neale Playlist

Video thumbnail

Science & Technology Q&A for Kids (and others) [Part 5]

Stephen Wolfram hosts an Ask Me Anything about science and technology for all ages. Originally livestreamed at: https://twitch.tv/stephen_wolfram Follow us on our official social media channels: Twitter: https://twitter.com/WolframResearch/ Facebook: https://www.facebook.com/wolframrese

From playlist Stephen Wolfram Ask Me Anything About Science & Technology

Video thumbnail

Using Clocks to Solve Fractions String 9

This string alternates between addition and subtraction

From playlist Arithmetic and Pre-Algebra: Fractions, Decimals and Percents

Video thumbnail

Catherine Greenhill (UNSW), The small subgraph conditioning method and hypergraphs, 26th May 2020

Speaker: Catherine Greenhill (UNSW) Title: The small subgraph conditioning method and hypergraphs Abstract: The small subgraph conditioning method is an analysis of variance technique which was introduced by Robinson and Wormald in 1992, in their proof that almost all cubic graphs are Ha

From playlist Seminars

Related pages

Equality (mathematics) | Tennenbaum's theorem | Operation (mathematics) | Infinite set | Unary operation | Gödel's incompleteness theorems | Gödel numbering | Non-standard model of arithmetic | Total order | Domain of a function | Extensionality | Axiom schema | Computable function | Peano axioms | Empty set | Injective function | Axiom of adjunction | Variable (mathematics) | Presburger arithmetic | Decidability (logic) | Recursive definition | Multiplication | Successor function | Natural number | Mathematics | Addition | Set (mathematics) | Second-order arithmetic | Mathematical induction | List of first-order theories | Skolem arithmetic | Complete theory | Axiom | Zermelo set theory | General set theory | Formal system | Gentzen's consistency proof | Cardinality | Binary operation | First-order logic | Set-theoretic definition of natural numbers