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2011 The Block Relation in Computable Linear Orders
Michael Moses
Notre Dame J. Formal Logic 52(3): 289-305 (2011). DOI: 10.1215/00294527-1435465

Abstract

The block relation B(x,y) in a linear order is satisfied by elements that are finitely far apart; a block is an equivalence class under this relation. We show that every computable linear order with dense condensation-type (i.e., a dense collection of blocks) but no infinite, strongly η-like interval (i.e., with all blocks of size less than some fixed, finite k) has a computable copy with the nonblock relation ¬B(x,y) computably enumerable. This implies that every computable linear order has a computable copy with a computable nontrivial self-embedding and that the long-standing conjecture characterizing those computable linear orders every computable copy of which has a computable nontrivial self-embedding (as precisely those that contain an infinite, strongly η-like interval) holds for all linear orders with dense condensation-type.

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Michael Moses. "The Block Relation in Computable Linear Orders." Notre Dame J. Formal Logic 52 (3) 289 - 305, 2011. https://doi.org/10.1215/00294527-1435465

Information

Published: 2011
First available in Project Euclid: 28 July 2011

zbMATH: 1260.03085
MathSciNet: MR2822490
Digital Object Identifier: 10.1215/00294527-1435465

Subjects:
Primary: 03D45
Secondary: 03C57

Keywords: block relation , computable linear order , self-embedding

Rights: Copyright © 2011 University of Notre Dame

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Vol.52 • No. 3 • 2011
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