Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/165558
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dc.contributor.authorTran, Hong Hanhen_US
dc.date.accessioned2023-03-30T00:51:19Z-
dc.date.available2023-03-30T00:51:19Z-
dc.date.issued2023-
dc.identifier.citationTran, H. H. (2023). Cupping in the computably enumerable degrees. Doctoral thesis, Nanyang Technological University, Singapore. https://hdl.handle.net/10356/165558en_US
dc.identifier.urihttps://hdl.handle.net/10356/165558-
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.language.isoenen_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
dc.identifier.doi10.32657/10356/165558-
dc.contributor.supervisoremailguohua@ntu.edu.sgen_US
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