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Title: Rice and Rice-Shapiro theorems for transfinite correction grammars
Authors: Case, J.
Jain, S. 
Keywords: Decidability
Recursion theory
Rice and Rice-Shapiro Theorems
Transfinite correction grammars
Issue Date: 2011
Citation: Case, J., Jain, S. (2011). Rice and Rice-Shapiro theorems for transfinite correction grammars. Mathematical Logic Quarterly 57 (5) : 504-516. ScholarBank@NUS Repository.
Abstract: Hay and, then, Johnson extended the classic Rice and Rice-Shapiro Theorems for computably enumerable sets, to analogs for all the higher levels in the finite Ershov Hierarchy. The present paper extends their work (with some motivations presented) to analogs in the transfinite Ershov Hierarchy. Some of the transfinite cases are done for all transfinite notations in Kleene's important system of notations. Other cases are done for all transfinite notations in a very natural, proper subsystem of, where has at least one notation for each constructive ordinal. In these latter cases it is open as to what happens for the entire set of transfinite notations in. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Source Title: Mathematical Logic Quarterly
ISSN: 09425616
DOI: 10.1002/malq.201020054
Appears in Collections:Staff Publications

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