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The jump of a Σ n ‐cut
Author(s) -
Chong C. T.,
Yang Yue
Publication year - 2007
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm016
Subject(s) - jump , environmental science , mathematics , physics , astronomy
Let n ⩾1. We study the proof‐theoretic strength of jump classes of the Turing degrees from the point of view of fragments of Peano arithmetic. By investigating the jump of a Σ n definable cut in a model of Δ n ‐induction, we show that over the base theory PA – + Δ n ‐induction, the existence of a non‐trivial low n Turing degree is equivalent to Σ n ‐induction.