Countable admissible ordinals and hyperdegrees
نویسندگان
چکیده
منابع مشابه
Countable Ordinals
This development defines a well-ordered type of countable ordinals. It includes notions of continuous and normal functions, recursively defined functions over ordinals, least fixed-points, and derivatives. Much of ordinal arithmetic is formalized, including exponentials and logarithms. The development concludes with formalizations of Cantor Normal Form and Veblen hierarchies over normal functions.
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Proof. For notational simplicity let us take n = 1 as a typical case. Thus let A C WO be ΣJ and assume sup {|a |: a E A} < Nj. Let B Qω be Π2 and /: ω ->ω recursive such that f[B] = A. Consider then the following game: Player I plays β, player II plays γ and II wins iff γ E WO&(β E B -> \f(β)| g | γ | ) . Clearly player II has a winning strategy in this game. But his payoff set is Σ\9 so by a r...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1976
ISSN: 0001-8708
DOI: 10.1016/0001-8708(76)90187-0