منابع مشابه
Vienna notes on effective descriptive set theory and admissible sets
These notes are based around the exposition of a sequence of connected ideas: ∆1 and Π 1 1 and Σ 1 1 sets; admissible structures; ω 1 ; recursive well founded relations; ordinal analysis of trees; Barwise compactness; Gandy-Harrington forcing. I am not going to discuss applications of these techniques – though there are striking applications such as Harrington’s proof of Silver’s theorem, or th...
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Best-response sets (Pearce [29, 1984]) characterize the epistemic condition of “rationality and common belief of rationality.” When rationality incorporates a weak-dominance (admissibility) requirement, the self-admissible set (SAS) concept (Brandenburger-Friedenberg-Keisler [18, 2008]) characterizes “rationality and common assumption of rationality.” We analyze the behavior of SAS’s in some ga...
متن کاملAdmissible digit sets
We examine a special case of admissible representations of the closed interval, namely those which arise via sequences of a finite number of Möbius transformations. We regard certain sets of Möbius transformations as a generalized notion of digits and introduce sufficient conditions that such a “digit set” yields an admissible representation of [0,+∞]. Furthermore we establish the productivity ...
متن کاملDense Admissible Sets
Call a set of integers {b1, b2, . . . , bk} admissible if for any prime p, at least one congruence class modulo p does not contain any of the bi. Let ρ ∗(x) be the size of the largest admissible set in [1, x]. The Prime k-tuples Conjecture states that any for any admissible set, there are infinitely many n such that n+b1, n+b2, . . . n+bk are simultaneously prime. In 1974, Hensley and Richards ...
متن کاملAdmissible Proof Theory And
1 Prologue Ordinals made their entrance in proof theory through Gentzen's second consistency proof for Peano Arithmetic by transsnite induction up to " 0 , the latter being applied only to decidable predicates (cf. Gentzen 1938]). Gentzen's constructive use of ordinals as a method of analyzing formal theories has come to be a paradigm for much of proof theory from then on, particularly as exemp...
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ژورنال
عنوان ژورنال: Annals of Mathematical Logic
سال: 1973
ISSN: 0003-4843
DOI: 10.1016/0003-4843(73)90009-0