 Determinacy in L(ℝ)Itay Neeman ()
Chapter 22 in Handbook of Set Theory, 2010, pp 1877-1950 from Springer Abstract: Abstract A two-player game is said to be determined if one of the two players has a winning strategy. Determinacy for a pointclass Γ is the assertion that all perfect information two-player games of length ω on natural numbers, with payoff in Γ, are determined. Determinacy may fail for games with payoff sets constructed using the axiom of choice, but turns out in contrast to be a key property of definable sets, from which many other properties and a rich structure theory can be derived. This paper presents proofs of determinacy for definable sets, starting with determinacy for the pointclass of analytic sets, continuing through projective sets, and ending with all sets in L(ℝ). Proofs of determinacy for these pointclasses involve large cardinal axioms at the level of measurable cardinals and Woodin cardinals. The paper presents some of the theory of these large cardinals, including the relevant definitions and all results that are needed for the determinacy proofs. Keywords: Direct Limit; Winning Strategy; Canonical Extension; Measurable Cardinal; Genericity Iteration (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4020-5764-9_23 Ordering information: This item can be ordered from DOI: 10.1007/978-1-4020-5764-9_23 Access Statistics for this chapter More chapters in Springer Books from Springer |
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