Limitwise monotonic functions, sets, and degrees on computable domains
Asher M. Kach and Daniel Turetsky
Source: J. Symbolic Logic Volume 75, Issue 1
(2010), 131-154.
Abstract
We extend the notion of limitwise monotonic functions to include arbitrary computable domains. We then study which sets and degrees are support increasing (support strictly increasing) limitwise monotonic on various computable domains. As applications, we provide a characterization of the sets S with computable increasing η-representations using support increasing limitwise monotonic sets on ℚ and note relationships between the class of order-computable sets and the class of support increasing (support strictly increasing) limitwise monotonic sets on certain domains.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1264433912
Digital Object Identifier: doi:10.2178/jsl/1264433912
Zentralblatt MATH identifier: 05681295
Mathematical Reviews number (MathSciNet): MR2605885
References
Richard J. Coles, Rod Downey, and Bakhadyr Khoussainov, On initial segments of computable linear orders, Order, vol. 14 (1997/98), no. 2, pp. 107--124.
Mathematical Reviews (MathSciNet): MR1631684
Digital Object Identifier: doi:10.1023/A:1006031314563
Barbara F. Csima, Denis R. Hirschfeldt, Julia F. Knight, and Robert I. Soare, Bounding prime models, Journal of Symbolic Logic, vol. 69 (2004), no. 4, pp. 1117--1142.
Mathematical Reviews (MathSciNet): MR2135658
Zentralblatt MATH: 1071.03021
Digital Object Identifier: doi:10.2178/jsl/1102022214
Project Euclid: euclid.jsl/1102022214
R. G. Downey, Computability theory and linear orderings, Handbook of Recursive Mathematics, Vol. 2, Studies in Logic and the Foundations of Mathematics, vol. 139, North-Holland, Amsterdam, 1998, pp. 823--976.
Mathematical Reviews (MathSciNet): MR1673590
Zentralblatt MATH: 0941.03045
Andrey N. Frolov and Maxim V. Zubkov, Increasing $\eta$-representable degrees, submitted.
Kenneth Harris, $\eta$-representations of sets and degrees, Journal of Symbolic Logic, vol. 73 (2008), no. 4, pp. 1097--1121.
Mathematical Reviews (MathSciNet): MR2467206
Zentralblatt MATH: 1158.03025
Digital Object Identifier: doi:10.2178/jsl/1230396908
Project Euclid: euclid.jsl/1230396908
Denis Hirschfeldt, Russell Miller, and Sergei Podzorov, Order-computable sets, Notre Dame Journal of Formal Logic, vol. 48 (2007), no. 3, pp. 317--347.
Mathematical Reviews (MathSciNet): MR2336351
Zentralblatt MATH: 1146.03030
Digital Object Identifier: doi:10.1305/ndjfl/1187031407
Project Euclid: euclid.ndjfl/1187031407
Asher M. Kach, Computable shuffle sums of ordinals, Archive for Mathematical Logic, vol. 47 (2008), no. 3, pp. 211--219.
Mathematical Reviews (MathSciNet): MR2415492
Zentralblatt MATH: 1149.03034
Digital Object Identifier: doi:10.1007/s00153-008-0077-3
N. G. Khisamiev, Criterion for constructivizability of a direct sum of cyclic $p$-groups, Izvestiya Akademii Nauk Kazakhskoi SSR. Seriya Fiziko-Matematicheskaya, vol. 1 (1981), no. 86, pp. 51--55.
Mathematical Reviews (MathSciNet): MR614069
--------, Constructive abelian groups, Handbook of Recursive Mathematics, Vol. 2, Studies in Logic and the Foundations of Mathematics, vol. 139, North-Holland, Amsterdam, 1998, pp. 1177--1231.
Mathematical Reviews (MathSciNet): MR1673602
Bakhadyr Khoussainov, Andre Nies, and Richard A. Shore, Computable models of theories with few models, Notre Dame Journal of Formal Logic, vol. 38 (1997), no. 2, pp. 165--178.
Mathematical Reviews (MathSciNet): MR1489408
Zentralblatt MATH: 0891.03013
Digital Object Identifier: doi:10.1305/ndjfl/1039724885
Project Euclid: euclid.ndjfl/1039724885
Manuel Lerman, On recursive linear orderings, Logic Year 1979--80 (Proceedings of Seminars and Conferences in Mathematical Logic, University of Connecticut, Storrs, Connecticut, 1979/80), Lecture Notes in Mathematics, vol. 859, Springer, Berlin, 1981, pp. 132--142.
Mathematical Reviews (MathSciNet): MR619867
Zentralblatt MATH: 0467.03045
Joseph G. Rosenstein, Linear orderings, Pure and Applied Mathematics, vol. 98, Academic Press [Harcourt Brace Jovanovich Publishers], New York, 1982.
Mathematical Reviews (MathSciNet): MR662564
Maxim Zubkov, On $\eta$-representable sets, Computation and Logic in the Real World, Third Conference on Computability in Europe (CiE), Lecture Notes in Computer Science, vol. 4497, 2007, pp. 364--366.
