The strength of Jullien's indecomposability theorem

Journal of Mathematical Logic 8 (1):93-119 (2008)
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Abstract

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 [Formula: see text] choice and [Formula: see text] comprehension.

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Citations of this work

Reverse mathematics: the playground of logic.Richard A. Shore - 2010 - Bulletin of Symbolic Logic 16 (3):378-402.
Necessary use of [image] induction in a reversal.Itay Neeman - 2011 - Journal of Symbolic Logic 76 (2):561 - 574.
The Strength of an Axiom of Finite Choice for Branches in Trees.G. O. H. Jun Le - 2023 - Journal of Symbolic Logic 88 (4):1367-1386.
Almost Theorems of Hyperarithmetic Analysis.Richard A. Shore - forthcoming - Journal of Symbolic Logic:1-33.

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References found in this work

Indecomposable linear orderings and hyperarithmetic analysis.Antonio Montalbán - 2006 - Journal of Mathematical Logic 6 (1):89-120.
On the Π1 1 -separation principle.Antonio Montalbán - 2008 - Mathematical Logic Quarterly 54 (6):563-578.
Linear Orderings.Joseph G. Rosenstein - 1983 - Journal of Symbolic Logic 48 (4):1207-1209.
Forcing with tagged trees.John R. Steel - 1978 - Annals of Mathematical Logic 15 (1):55.

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