Determinacy

Set theory, Mathematics, Lookup table, Baire space (set theory), Topology, Inner model
Herausgegeben:Angelus, Jerold

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Verlag: Alphascript Publishing / Duct Publishing
• Aufl.
• Seitenzahl: 64
• Englisch
• ISBN-13: 9786138244639
• ISBN-10: 613824463X
• Artikelnr.: 34709704