Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Recent work has clarified how various natural second-order set-theoretic principles, such as those concerned with class forcing or with proper class games, fit into a new robust hierarchy of second-order set theories between Gödel-Bernays GBC set theory and Kelley-Morse KM set theory and beyond. For example, the principle of clopen determinacy for proper class games is exactly equivalent to the principle of elementary transfinite recursion ETR, strictly between GBC and GBC+$\Pi^1_1$-comprehension; open determinacy for class games, in contrast, is strictly stronger; meanwhile, the class forcing theorem, asserting that every class forcing notion admits corresponding forcing relations, is strictly weaker, and is exactly equivalent to the fragment $\text{ETR}_{\text{Ord}}$ and to numerous other natural principles. What is emerging is a higher set-theoretic analogue of the familiar reverse mathematics of second-order number theory. Recent work has clarified how various natural second-order set-theoretic principles, such as those concerned with class forcing or with proper class games, fit into a new robust hierarchy of second-order set theories between Gödel-Bernays GBC set theory and Kelley-Morse KM set theory and beyond. For example, the principle of clopen determinacy for proper class games is exactly equivalent to the principle of elementary transfinite recursion ETR, ...

03E60 ; 03E30 ; 03C62

Filtrer

Domaine
Codes MSC
Audience

Z
class="contents">

Documentation mathématique

Services numériques pour les mathématiques

  • |
  • liste des Conferenciers
  • |
  • Domaines
  • |
  • Recherche
  • G

    F Nous contacter


    0

    Documents  03E60 | enregistrements trouvés : 1

    O
       

    -A +A

    P Q