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A Tale of Two Set Theories

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21730%2F19%3A00339803" target="_blank" >RIV/68407700:21730/19:00339803 - isvavai.cz</a>

  • Result on the web

    <a href="https://doi.org/10.1007/978-3-030-23250-4_4" target="_blank" >https://doi.org/10.1007/978-3-030-23250-4_4</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1007/978-3-030-23250-4_4" target="_blank" >10.1007/978-3-030-23250-4_4</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    A Tale of Two Set Theories

  • Original language description

    We describe the relationship between two versions of Tarski-Grothendieck set theory: the first-order set theory of Mizar and the higher-order set theory of Egal. We show how certain higher-order terms and propositions in Egal have equivalent first-order presentations. We then prove Tarski’s Axiom A (an axiom in Mizar) in Egal and construct a Grothendieck Universe operator (a primitive with axioms in Egal) in Mizar.

  • Czech name

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

  • OECD FORD branch

    10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Result continuities

  • Project

  • Continuities

    R - Projekt Ramcoveho programu EK

Others

  • Publication year

    2019

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Article name in the collection

    Intelligent Computer Mathematics

  • ISBN

    978-3-030-23249-8

  • ISSN

    0302-9743

  • e-ISSN

    1611-3349

  • Number of pages

    17

  • Pages from-to

    44-60

  • Publisher name

    Springer

  • Place of publication

    Cham

  • Event location

    Prague

  • Event date

    Jul 8, 2019

  • Type of event by nationality

    WRD - Celosvětová akce

  • UT code for WoS article