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).
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
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"
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
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
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
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
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
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
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
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
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
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
(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
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)
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