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Title: Cupping in the computably enumerable degrees
Authors: Tran, Hong Hanh
Keywords: Science::Mathematics::Mathematical logic
Issue Date: 2023
Publisher: Nanyang Technological University
Source: Tran, H. H. (2023). Cupping in the computably enumerable degrees. Doctoral thesis, Nanyang Technological University, Singapore.
Abstract: This 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.
DOI: 10.32657/10356/165558
Schools: School of Physical and Mathematical Sciences 
Rights: This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Theses

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