Uniformity in the Recursively Enumerable Degrees and Infima in the Degrees of the Differences of Recursively Enumberable Sets
Author: Deborah Suzanne Kaddah
Publisher:
Published: 1992
Total Pages: 226
ISBN-13:
DOWNLOAD EBOOK →Author: Deborah Suzanne Kaddah
Publisher:
Published: 1992
Total Pages: 226
ISBN-13:
DOWNLOAD EBOOK →Author: Noam Greenberg
Publisher: American Mathematical Soc.
Published: 2006
Total Pages: 114
ISBN-13: 0821838857
DOWNLOAD EBOOK →When attempting to generalize recursion theory to admissible ordinals, it may seem as if all classical priority constructions can be lifted to any admissible ordinal satisfying a sufficiently strong fragment of the replacement scheme. We show, however, that this is not always the case. In fact, there are some constructions which make an essential use of the notion of finiteness which cannot be replaced by the generalized notion of $\alpha$-finiteness. As examples we discuss bothcodings of models of arithmetic into the recursively enumerable degrees, and non-distributive lattice embeddings into these degrees. We show that if an admissible ordinal $\alpha$ is effectively close to $\omega$ (where this closeness can be measured by size or by cofinality) then such constructions maybe performed in the $\alpha$-r.e. degrees, but otherwise they fail. The results of these constructions can be expressed in the first-order language of partially ordered sets, and so these results also show that there are natu
Author: Robert I. Soare
Publisher: Springer
Published: 2014-08-23
Total Pages: 437
ISBN-13: 9783540666813
DOWNLOAD EBOOK →..."The book, written by one of the main researchers on the field, gives a complete account of the theory of r.e. degrees. .... The definitions, results and proofs are always clearly motivated and explained before the formal presentation; the proofs are described with remarkable clarity and conciseness. The book is highly recommended to everyone interested in logic. It also provides a useful background to computer scientists, in particular to theoretical computer scientists." Acta Scientiarum Mathematicarum, Ungarn 1988 ..."The main purpose of this book is to introduce the reader to the main results and to the intricacies of the current theory for the recurseively enumerable sets and degrees. The author has managed to give a coherent exposition of a rather complex and messy area of logic, and with this book degree-theory is far more accessible to students and logicians in other fields than it used to be." Zentralblatt für Mathematik, 623.1988
Author: R.I.·索尔 (美)
Publisher:
Published: 1987
Total Pages: 437
ISBN-13: 9787030182951
DOWNLOAD EBOOK →Author: American Mathematical Society
Publisher:
Published: 1993
Total Pages: 998
ISBN-13:
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