Automorphisms of η-Like Computable Linear Orderings and Kierstead’s Conjecture

Charles Harris; Kyung Il Lee; S. Barry  Cooper

doi:10.1002/malq.201400109

Automorphisms of η-Like Computable Linear Orderings and Kierstead’s Conjecture

Charles Harris
, Kyung Il Lee
, S. Barry Cooper

Research output: Contribution to journal › Article (Academic Journal) › peer-review

4 Citations (Scopus)

415 Downloads (Pure)

Abstract

We develop an approach to the longstanding conjecture of H.A. Kierstead concerning the character of strongly nontrivial automorphisms of computable linear orderings. Our main result is that for any η-like computable linear ordering B, such that B has no interval of order type η, and such that the order type of B is determined by a 0′-limitwise monotonic maximal block function, there exists computable L isomorphic to B such that L has no nontrivial Π^0_1 automorphism.

Original language	English
Pages (from-to)	481-506
Number of pages	26
Journal	Mathematical Logic Quarterly
Volume	62
Issue number	6
Early online date	29 Dec 2016
DOIs	https://doi.org/10.1002/malq.201400109
Publication status	Published - Dec 2016

Bibliographical note

Date of Acceptance: 25/04/2015

Keywords

Computable,
linear ordering,
automorphism,
rigidity

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10.1002/malq.201400109

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title = "Automorphisms of η-Like Computable Linear Orderings and Kierstead{\textquoteright}s Conjecture",

abstract = "We develop an approach to the longstanding conjecture of H.A. Kierstead concerning the character of strongly nontrivial automorphisms of computable linear orderings. Our main result is that for any η-like computable linear ordering B, such that B has no interval of order type η, and such that the order type of B is determined by a 0′-limitwise monotonic maximal block function, there exists computable L isomorphic to B such that L has no nontrivial Π\textasciicircum{}0\_1 automorphism.",

keywords = "Computable,, linear ordering,, automorphism,, rigidity",

author = "Charles Harris and Lee, \{Kyung Il\} and Cooper, \{S. Barry\}",

note = "Date of Acceptance: 25/04/2015",

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language = "English",

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AU - Harris, Charles

AU - Lee, Kyung Il

AU - Cooper, S. Barry

N1 - Date of Acceptance: 25/04/2015

PY - 2016/12

Y1 - 2016/12

N2 - We develop an approach to the longstanding conjecture of H.A. Kierstead concerning the character of strongly nontrivial automorphisms of computable linear orderings. Our main result is that for any η-like computable linear ordering B, such that B has no interval of order type η, and such that the order type of B is determined by a 0′-limitwise monotonic maximal block function, there exists computable L isomorphic to B such that L has no nontrivial Π^0_1 automorphism.

AB - We develop an approach to the longstanding conjecture of H.A. Kierstead concerning the character of strongly nontrivial automorphisms of computable linear orderings. Our main result is that for any η-like computable linear ordering B, such that B has no interval of order type η, and such that the order type of B is determined by a 0′-limitwise monotonic maximal block function, there exists computable L isomorphic to B such that L has no nontrivial Π^0_1 automorphism.

KW - Computable,

KW - linear ordering,

KW - automorphism,

KW - rigidity

U2 - 10.1002/malq.201400109

DO - 10.1002/malq.201400109

M3 - Article (Academic Journal)

SN - 0942-5616

VL - 62

SP - 481

EP - 506

JO - Mathematical Logic Quarterly

JF - Mathematical Logic Quarterly

IS - 6

ER -

Automorphisms of η-Like Computable Linear Orderings and Kierstead’s Conjecture

Abstract

Bibliographical note

Keywords

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