Articles by Author: G Van Der Horst

Search results for G Van Der Horst

We found 34 results for you
  1. ESSENTIALLY ALGEBRAIC CATEGORIES

    ESSENTIALLY ALGEBRAIC CATEGORIES

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    Various familiar concepts of algebraic categories (such as primitive and quasiprimitive categories of algebras as well as varietal, monadic, regular monadic, and regular categories) are contrasted with each other and with the new notion of essentially algebraic categories.
  2. ÜBER DIE UNGLEICHUNG ZWISCHEN DEM GEOMETRISCHEN UND DEM ARITHMETISCHEN MITTEL

    ÜBER DIE UNGLEICHUNG ZWISCHEN DEM GEOMETRISCHEN UND DEM ARITHMETISCHEN MITTEL

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    The arithmetic mean—geometric mean inequality states
  3. REMARKS ON CATEGORIES OF ALGEBRAS DEFINED BY A PROPER CLASS OF OPERATIONS

    REMARKS ON CATEGORIES OF ALGEBRAS DEFINED BY A PROPER CLASS OF OPERATIONS

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    A category A of algebras is constructed, which has the following features:
  4. AN EXTENSION AND A CONVERSE OF KY FAN'S INEQUALITY

    AN EXTENSION AND A CONVERSE OF KY FAN'S INEQUALITY

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    Let An and Gn (resp. A'n and G'n) be the weighted arithmetic and geometric means of x1,….xn (resp. 1-x1,…,1-xn) with x1 ε(0.1/2]. i = 1,…,n. Then we have
  5. MAXIMAL FILTERS, CONTINUITY AND CHOICE PRINCIPLES

    MAXIMAL FILTERS, CONTINUITY AND CHOICE PRINCIPLES

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    In Zermelo-Fraenkel set theory ZF without the Axiom of Choice AC, results such as the following are established:
  6. Striking differences between ZF and ZF+weak choice in view of metric spaces

    Striking differences between ZF and ZF+weak choice in view of metric spaces

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    Well-known properties held by metric spaces with the countable chain condition (ccc) such as separability, second countability, Lindelöf, paracompactness may fail in the absence of the axiom of choice AC. In the long catalogue of weak choice principles, see [10],...
  7. On Closure Operators, the Reals, and Choice

    On Closure Operators, the Reals, and Choice

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    The behaviour and the relationships between various closure operators are investigated for subspaces of the reals in the setting of ZF, i. e., Zermelo-Fraenkel set theory without the axiom of choice. Typical results: Equivalent are: 1. Every subspace...
  8. Graph-Coloring and Choice a Note on a Note by Shelah and Soifer

    Graph-Coloring and Choice a Note on a Note by Shelah and Soifer

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    Sharpening results of Shelah and Soifer we will show that in ZF set theory the Shelah-Soifer Graph G has the following properties: 1. If AC(2), the axiom of choice for families of 2-element sets, or AC(R), the axiom...