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On computable self-embeddings of computable linear orderings

Published online by Cambridge University Press:  12 March 2014

Rodney G. Downey ,
Bart Kastermans  and
Steffen Lempp
Rodney G. Downey
Affiliation:
School of Mathematics, Statistics and Computer Science, Victoria University, Wellington 6140, New Zealand, E-mail: Rod.Downey@mcs.vuw.ac.nz
Bart Kastermans
Affiliation:
Department of Mathematics, University of Colorado, Boulder, Co 80309-0395, USA, E-mail: bart.kastermans@colorado.edu
Steffen Lempp
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wi 53706-1388, USA, E-mail: lempp@math.wisc.edu
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Abstract

We solve a longstanding question of Rosenstein, and make progress toward solving a long-standing open problem in the area of computable linear orderings by showing that every computable η-like linear ordering without an infinite strongly η-like interval has a computable copy without nontrivial computable self-embedding.

The precise characterization of those computable linear orderings which have computable copies without nontrivial computable self-embedding remains open.

Keywords

computable linear orderingself-embedding
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 4 , December 2009 , pp. 1352 - 1366
Copyright
Copyright © Association for Symbolic Logic 2009

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