Abstract
The paper gives an overview over recent results of the author on various upper semilattices of many-one degrees. The local isomorphism type (i.e. the collection of isomorphism types of all principal ideals) of m-degrees belonging to any fixed class of arithmetical hierarchy is completely described. The description of the semilattices of simple, hypersimple and \(\Delta^0_2\) m-degrees up to isomorphism is also given.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Denisov, S.D.: Structure of the upper semilattice of recursively enumerable m-degrees and related questions. I. Algebra and Logic 17, 418–443 (1978)
Ershov, Y.L.: Hyperhypersimple m-degrees. Algebra i Logika 8, 523–552 [in Russian] (1969)
Ershov, Y.L.: The upper semilattice of numerations of a finite set. Algebra and Logic 14, 159–175 (1975)
Ershov, Y.L.: Numbering theory. Nauka, Moskow [in Russian] (1977)
Grätzer, G.: Generall lattice theory. Birkhäuser Verlag, Basel (1998)
Lachlan, A.: Recursively enumerable many-one degrees. Algebra and Logic 11, 186–202 (1972)
Odifreddi, P.: Classical recursion theory, vol. II. Elsevier, Amsterdam (1999)
Podzorov, S.Y.: On the local structure of Rogers semilattices of Σ 0 n -computable numberings. Algebra and Logic 44, 82–94 (2005)
Podzorov, S.Y.: Numbered distributive semilattices. Siberian Adv. in Math 17, 171–185 (2007)
Podzorov, S.Y.: The universal Lachlan semilattice without the greatest element. Algebra and Logic 46, 163–187 (2007)
Podzorov, S.Y.: Arithmetical m-degrees. Siberian Math. J. (submitted), http://www.nsu.ru/education/podzorov/Arithm.pdf
Rogers, H.: Theory of recursive functions and effective computability. McGraw-Hill Book Company, New York (1967)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Podzorov, S. (2008). Upper Semilattices in Many-One Degrees. In: Beckmann, A., Dimitracopoulos, C., Löwe, B. (eds) Logic and Theory of Algorithms. CiE 2008. Lecture Notes in Computer Science, vol 5028. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69407-6_53
Download citation
DOI: https://doi.org/10.1007/978-3-540-69407-6_53
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69405-2
Online ISBN: 978-3-540-69407-6
eBook Packages: Computer ScienceComputer Science (R0)