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On computable self-embeddings of computable linear orderings

Published online by Cambridge University Press:  12 March 2014

Rodney G. Downey
Affiliation:
School of Mathematics, Statistics and Computer Science, Victoria University, Wellington 6140, New Zealand, E-mail: [email protected]
Bart Kastermans
Affiliation:
Department of Mathematics, University of Colorado, Boulder, Co 80309-0395, USA, E-mail: [email protected]
Steffen Lempp
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wi 53706-1388, USA, E-mail: [email protected]

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.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2009

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