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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Recursive linear orders with incomplete successivities


Authors: Rodney G. Downey and Michael F. Moses
Journal: Trans. Amer. Math. Soc. 326 (1991), 653-668
MSC: Primary 03D45; Secondary 03C57, 06A05
MathSciNet review: 1005933
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Abstract: A recursive linear order is said to have intrinsically complete successivities if, in every recursive copy, the successivities form a complete set. We show (Theorem 1) that there is a recursive linear order with intrinsically complete successivities but (Theorem 2) that this cannot be a discrete linear oder. We investigate the related issues of intrinsically non-low and non-semilow successivities in discrete linear orders. We show also (Theorem 3) that no recursive linear order has intrinsically $ wtt$-complete successivities.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1991-1005933-2
PII: S 0002-9947(1991)1005933-2
Article copyright: © Copyright 1991 American Mathematical Society