Ellen Hammatt
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View article: LATTICE EMBEDDINGS AND PUNCTUAL LINEAR ORDERS
LATTICE EMBEDDINGS AND PUNCTUAL LINEAR ORDERS Open
We investigate the primitive recursive content of linear orders. We prove that the punctual degrees of rigid linear orders, the order of the integers $\mathbb {Z}$ , and the order of the rationals $\mathbb {Q}$ embed the diamond (preservin…
View article: Arriving on Time: Punctuality in Structures, Isomorphisms and 1-Decidability
Arriving on Time: Punctuality in Structures, Isomorphisms and 1-Decidability Open
This thesis contributes to the area of computable structure theory. In particular, it contributes to the study of punctual structures; the systematic study of the primitive recursive content of mathematics initiated by Kalimullin, Melnikov…
View article: Hierarchy of Computably Enumerable Degrees II
Hierarchy of Computably Enumerable Degrees II Open
A transfinite hierarchy of Turing degrees of c.e.\ sets has been used to calibrate the dynamics of families of constructions in computability theory, and yields natural definability results. We review the main results of the area, and disc…
View article: Collapse in a Transfinite Hierarchy of Turing Degrees
Collapse in a Transfinite Hierarchy of Turing Degrees Open
In [2], Downey and Greenberg use the ordinals below ε0 to bound the number of mind-changes of computable approximations. This gives rise to a new transfinite hierarchy in the c.e. degrees; the totally α-c.a. degrees. This hierarchy is sign…
View article: Collapse in a Transfinite Hierarchy of Turing Degrees
Collapse in a Transfinite Hierarchy of Turing Degrees Open
In [2], Downey and Greenberg use the ordinals below ε0 to bound the number of mind-changes of computable approximations. This gives rise to a new transfinite hierarchy in the c.e. degrees; the totally α-c.a. degrees. This hierarchy is sign…