The Strength of Jullien’s Indecomposability Theorem
نویسنده
چکیده
Jullien’s indecomposability theorem states that if a scattered countable linear order is indecomposable, then it is either indecomposable to the left, or indecomposable to the right. The theorem was shown by Montalbán to be a theorem of hyperarithmetic analysis. We identify the strength of the theorem relative to standard reverse mathematics markers. We show that it lies strictly between weak Σ 1 choice and ∆ 1 comprehension. §
منابع مشابه
Necessary use of Σ¹₁ induction in a reversal
Jullien’s indecomposability theorem states that if a scattered countable linear order is indecomposable, then it is either indecomposable to the left, or indecomposable to the right. The theorem was shown by Montalbán to be a theorem of hyperarithmetic analysis, and then, in the base system RCA0 plus Σ 1 1 induction, it was shown by Neeman to have strength strictly between weak Σ 1 choice and ∆...
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تاریخ انتشار 2008