Sökning: "constructive algebra"

Visar resultat 1 - 5 av 23 avhandlingar innehållade orden constructive algebra.

  1. 1. On Constructive Sets and Partial Structures

    Författare :Olov Wilander; Erik Palmgren; Viggo Stoltenberg-Hansen; Bas Spitters; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematical Logic; Matematisk logik;

    Sammanfattning : The first three papers in this thesis study the formalisation of a set in type theory as a data type with an equivalence relation – an object usually known as a setoid. The corresponding formalisation of a locally small category is called an E-category. LÄS MER

  3. 2. Contributions to Pointfree Topology and Apartness Spaces

    Författare :Anton Hedin; Erik Palmgren; Viggo Stoltenberg-Hansen; Peter Schuster; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Constructive mathematics; General topology; Pointfree topology; Domain theory; Interval analysis; Apartness spaces; Mathematical logic; Matematisk logik; Mathematical Logic; Matematisk logik;

    Sammanfattning : The work in this thesis contains some contributions to constructive point-free topology and the theory of apartness spaces. The first two papers deal with constructive domain theory using formal topology. LÄS MER

  4. 3. Representation theorems for abelian and model categories

    Författare :Anna Giulia Montaruli; Peter LeFanu Lumsdaine; Gregory Arone; Marek Zawadowski; Stockholms universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Category Theory; Logic; Algebra; Homotopy Theory; matematik; Mathematics;

    Sammanfattning : In this PhD thesis we investigate a representation theorem for small abelian categories and a representation theorem for left proper, enriched model categories, with the purpose of describing them concretely in terms of specific well-known categories.For the abelian case, we study the constructivity issues of the Freyd-Mitchell Embedding Theorem, which states the existence of a full embedding from a small abelian category into the category of modules over an appropriate ring. LÄS MER

  5. 4. A Natural Interpretation of Classical Proofs

    Författare :Jens Brage; Per Martin-Löf; Sara Negri; Stockholms universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Brouwer-Heyting-Kolmogorov; classical logic; constructive type theory; constructive semantics; proof interpretation; double-negation; continuation-passing-style; natural deduction; sequent calculus; cut elimination; explicit substitution; Mathematical logic; Matematisk logik;

    Sammanfattning : In this thesis we use the syntactic-semantic method of constructive type theory to give meaning to classical logic, in particular Gentzen's LK.We interpret a derivation of a classical sequent as a derivation of a contradiction from the assumptions that the antecedent formulas are true and that the succedent formulas are false, where the concepts of truth and falsity are taken to conform to the corresponding constructive concepts, using function types to encode falsity. LÄS MER

  7. 5. Achieving completeness: from constructive set theory to large cardinals

    Författare :Christian Espíndola; Erik Palmgren; Benno van den Berg; Stockholms universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematics; matematik;

    Sammanfattning : This thesis is an exploration of several completeness phenomena, both in the constructive and the classical settings. After some introductory chapters in the first part of the thesis where we outline the background used later on, the constructive part contains a categorical formulation of several constructive completeness theorems available in the literature, but presented here in an unified framework. LÄS MER