Normal forms (logic)

Herbrandization

The Herbrandization of a logical formula (named after Jacques Herbrand) is a construction that is dual to the Skolemization of a formula. Thoralf Skolem had considered the Skolemizations of formulas in prenex form as part of his proof of the Löwenheim–Skolem theorem (Skolem 1920). Herbrand worked with this dual notion of Herbrandization, generalized to apply to non-prenex formulas as well, in order to prove Herbrand's theorem (Herbrand 1930). The resulting formula is not necessarily equivalent to the original one. As with Skolemization, which only preserves satisfiability, Herbrandization being Skolemization's dual preserves validity: the resulting formula is valid if and only if the original one is. (Wikipedia).

Video thumbnail

Introduction to Botany

Plants are remarkable organisms. From the tiniest shrub to the tallest tree, these organisms have fascinating structures and biological functions. What anatomical features do plants all have in common? What is the evolutionary history of plants? How do plants interact with their environmen

From playlist Botany

Video thumbnail

Recursive Factorial Function

Introduction to recursion.

From playlist Computer Science

Video thumbnail

Graham Leigh: On the computational content of classical sequent calculus

The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: Computational interpretations of classical logic are entwined with constructive proofs of Herbrand's Theorem which states, its simplest form, that for every valid existen

From playlist Workshop: "Proofs and Computation"

Video thumbnail

Angiosperms: Flowering Plants

We just learned about gymnosperms, and the incredible evolutionary advantages they had over their ancestors. But the next leap forward for plants was even more impressive. Angiosperms are flowering plants, so any plant with flowers or fruits is an angiosperm. And instead of fertilizing by

From playlist Botany

Video thumbnail

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

Video thumbnail

Michael Temkin - Wild coverings of Berkovich curves

I will describe the structure of finite morphisms between smooth Berkovich curves. The tame case is well known so the accent will be on the wild case. In particular, I will describe the loci of points of multiplicity n and their relation to Herbrand function and the ramification theory. If

From playlist A conference in honor of Arthur Ogus on the occasion of his 70th birthday

Video thumbnail

Artur Avila "Poincaré series and renormalization"

Originaire du Brésil, Artur Avila obtient son doctorat en 2001 à l'IMPA. En 2008 il reçoit le prix de l'EMS puis le Grand Prix Jacques Herbrand de l'Académie des sciences en 2009. Il a été conférencier plénier au Congrès international des mathématiciens en 2010. Il est Directeur de Recherc

From playlist Colloque Scientifique International Poincaré 100

Video thumbnail

Nalini Anantharaman "From the three-body problem to quantum mechanics"

Résumé Poincaré annonçait, dans l'introduction des Méthodes nouvelles de la mécanique céleste, fournit « un terrain solide sur lequel on pourra s'appuyer avec confiance ». C'est avec cette confiance que les physiciens du début du 20ème siècle se sont attaqués à l'étude de l'atome d'hélium,

From playlist Colloque Scientifique International Poincaré 100

Video thumbnail

Field Definition (expanded) - Abstract Algebra

The field is one of the key objects you will learn about in abstract algebra. Fields generalize the real numbers and complex numbers. They are sets with two operations that come with all the features you could wish for: commutativity, inverses, identities, associativity, and more. They

From playlist Abstract Algebra

Video thumbnail

Uses of Plant Hormones | Plants | Biology | FuseSchool

Uses of Plant Hormones | Plants | Biology | FuseSchool In this video we are going to look at a few different ways in which plant hormones can be used. Plant growth hormones (auxins) can be used as selective weedkillers. The selective weedkillers contain growth hormones, that cause the w

From playlist BIOLOGY: Agriculture

Video thumbnail

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

Video thumbnail

Plant Anatomy and Structure

We've learned about the types of plant cells, and the types of plant tissues, so the next step up on the hierarchy of organization is organs and organ systems. Plants have these too! The stem, the leaves, the roots, these are all considered organs of the plant, and they are organized into

From playlist Botany

Video thumbnail

Potential Automorphy - Richard Taylor

Richard Taylor Institute for Advanced Study October 4, 2010 I will introduce l-adic representations and what it means for them to be automorphic, talk about potential automorphy as an alternative to automorphy, explain what can currently be proved (but not how) and discuss what seem to me

From playlist Mathematics

Video thumbnail

(ML 7.7.A1) Dirichlet distribution

Definition of the Dirichlet distribution, what it looks like, intuition for what the parameters control, and some statistics: mean, mode, and variance.

From playlist Machine Learning

Video thumbnail

Finding Eigenvalues and Eigenvectors

In studying linear algebra, we will inevitably stumble upon the concept of eigenvalues and eigenvectors. These sound very exotic, but they are very important not just in math, but also physics. Let's learn what they are, and how to find them! Script by Howard Whittle Watch the whole Math

From playlist Mathematics (All Of It)

Video thumbnail

Hugo Duminil Copin - Compter les chemins auto-évitants sur le réseau en nid d'abeille

IHES, Prix Jacques Herbrand 2017 Réalisation technique : Antoine Orlandi (GRICAD) | Tous droits réservés

From playlist Des mathématiciens primés par l'Académie des Sciences 2017

Related pages

Duality (mathematics) | Löwenheim–Skolem theorem | Predicate functor logic | Jean van Heijenoort | Satisfiability | Logical equivalence | Thoralf Skolem | Validity (logic) | First-order logic | Jacques Herbrand