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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On Kierstead's conjecture


Authors: Keng Meng Ng and Maxim Zubkov
Journal: Trans. Amer. Math. Soc. 372 (2019), 3713-3753
MSC (2010): Primary 03C57, 03D45
DOI: https://doi.org/10.1090/tran/7858
Published electronically: May 9, 2019
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Abstract: We settle the long-standing Kierstead conjecture in the negative. We do this by constructing a computable linear order with no rational subintervals, where every block has order type finite or $ \zeta $, and where every computable copy has a strongly nontrivial $ \Pi ^0_1$ automorphism. We also construct a strongly $ \eta $-like linear order where every block has size at most $ 4$ with no rational subinterval such that every $ \Delta ^0_2$ isomorphic computable copy has a nontrivial $ \Pi ^0_1$ automorphism.


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Additional Information

Keng Meng Ng
Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371

Maxim Zubkov
Affiliation: N.I. Lobachevsky Institute of Mathematics and Mechanics, Kazan Federal University, Kremlevskaya 18, Kazan 420008, Russia

DOI: https://doi.org/10.1090/tran/7858
Keywords: Computable linear order, automorphism, Kierstead's conjecture
Received by editor(s): August 15, 2018
Received by editor(s) in revised form: March 30, 2019
Published electronically: May 9, 2019
Additional Notes: The first author was partially supported by grants MOE-RG131/17 and MOE2015-T2-2-055
The second author was supported by an RSF grant (project 18-11-00028)
Article copyright: © Copyright 2019 American Mathematical Society