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Title: The theory of the α degrees is undecidable
Authors: Chong, C.T. 
Slaman, T.A.
Issue Date: 2010
Citation: Chong, C.T., Slaman, T.A. (2010). The theory of the α degrees is undecidable. Israel Journal of Mathematics 178 (1) : 229-252. ScholarBank@NUS Repository.
Abstract: Let α be an arbitrary Σ1-admissible ordinal. For each n, there is a formula φn(x→, y→) such that for any relation R on a finite set F with n elements, there are α-degrees p→ such that the relation defined by φn(x→, p→) is isomorphic to R. Consequently, the theory of α-degrees is undecidable. © 2010 Hebrew University Magnes Press.
Source Title: Israel Journal of Mathematics
ISSN: 00212172
DOI: 10.1007/s11856-010-0064-3
Appears in Collections:Staff Publications

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