Please use this identifier to cite or link to this item:
Full metadata record
DC FieldValueLanguage
dc.contributor.authorTran, Hong Hanhen_US
dc.identifier.citationTran, H. H. (2023). Cupping in the computably enumerable degrees. Doctoral thesis, Nanyang Technological University, Singapore.
dc.description.abstractThis thesis is mainly concerned with the cupping property in the computably enumerable (c.e.) degrees. In particular, we study major sub-degrees, n-cuppable degrees and the quotient structure R/Ncup. In the first part, we present a direct construction of a cuppable high c.e. h with a low major sub-degree l such that h>= a for a given c.e. degree a. In the second part, we generalize the technique of Bie and Wu, used in the construction of a minimal pair in R/Ncup which is also a minimal pair in M/Ncup, to construct three incomplete c.e. degrees which are 2-cuppable but not 3-cuppable. This result will be directly generalized to arbitrary n>3 c.e. degrees. Consequently, for any n>0, there are n degrees which are (n-1)-cuppable but not n-cuppable. In the third part, using Bie and Wu's technique, we prove a claim by Li, Wu and Yang that the diamond lattice can be embedded in R/Ncup preserving 0 and 1.en_US
dc.publisherNanyang Technological Universityen_US
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).en_US
dc.subjectScience::Mathematics::Mathematical logicen_US
dc.titleCupping in the computably enumerable degreesen_US
dc.typeThesis-Doctor of Philosophyen_US
dc.contributor.supervisorWu Guohuaen_US
dc.contributor.schoolSchool of Physical and Mathematical Sciencesen_US
dc.description.degreeDoctor of Philosophyen_US
item.fulltextWith Fulltext-
Appears in Collections:SPMS Theses
Files in This Item:
File Description SizeFormat 
HanhThesisAmended.pdf1.59 MBAdobe PDFThumbnail

Page view(s)

Updated on Jun 15, 2024

Download(s) 50

Updated on Jun 15, 2024

Google ScholarTM




Items in DR-NTU are protected by copyright, with all rights reserved, unless otherwise indicated.