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Determinacy

  • Couverture cartonnée
  • 64 Nombre de pages
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In... Lire la suite
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Description

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In set theory, a branch of mathematics, determinacy is the study of under what circumstances one or the other player of a game must have a winning strategy, and the consequences of the existence of such strategies. The first sort of game we shall consider is the two-player game of perfect information of length , in which the players play natural numbers. In this sort of game we consider two players, often named I and II, who take turns playing natural numbers, with I going first. They play "forever"; that is, their plays are indexed by the natural numbers. When they're finished, a predetermined condition decides which player won. This condition need not be specified by any definable rule; it may simply be an arbitrary (infinitely long) lookup table saying who has won given a particular sequence of plays. More formally, consider a subset A of Baire space; recall that the latter consists of all -sequences of natural numbers. Then in the game GA, I plays a natural number a0, then II plays a1, then I plays a2, and so on.

Informations sur le produit

Titre: Determinacy
Éditeur:
Code EAN: 9786138244639
ISBN: 978-613-8-24463-9
Format: Couverture cartonnée
Editeur: Alphascript Publishing
Genre: Sciences naturelles en général
nombre de pages: 64
Poids: 104g
Taille: H229mm x B152mm x T4mm
Année: 2011
Auflage: Aufl.