Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/34682
Title: On Silver's Dichotomy
Authors: LI YANFANG
Keywords: Silver's Dichotomy, effectiveness, gandy-harrington forcing, pi1-1ca0
Issue Date: 12-Apr-2012
Source: LI YANFANG (2012-04-12). On Silver's Dichotomy. ScholarBank@NUS Repository.
Abstract: In this thesis, effectiveness of Silver's Dichotomy is investigated. Following Harrington's proof of Silver's Dichotomy, Silver's result is strengthened by showing that the reduction map from equality relation on 2^\omega to a given \Pi_1^1 equivalence relation E is recursive in Kleenes' O. Further more, another version of Silver's Dichotomy is proved and the reverse mathematics strength of this version of Silver's Dichotomy is examined. In particular, using model theoretic method, it is shown that this version of Silver's Dichotomy does not require \Pi_1^1 comprehension.
URI: http://scholarbank.nus.edu.sg/handle/10635/34682
Appears in Collections:Ph.D Theses (Open)

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