The Role of True Finiteness in the Admissible Recursively Enumerable Degrees is popular PDF and ePub book, written by Noam Greenberg in 2006, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, The Role of True Finiteness in the Admissible Recursively Enumerable Degrees can be Read Online from any device for your convenience.
The Role of True Finiteness in the Admissible Recursively Enumerable Degrees Book PDF Summary
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
Detail Book of The Role of True Finiteness in the Admissible Recursively Enumerable Degrees PDF
- Author : Noam Greenberg
- Release : 20 September 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821838853
- Genre : Mathematics
- Total Page : 114 pages
- Language : English
- PDF File Size : 17,8 Mb
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