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https://hdl.handle.net/2142/86790
Description
Title
Decision Problems in the Lattice of P01 Classes
Author(s)
Lawton, Linda Barker
Issue Date
2002
Doctoral Committee Chair(s)
Jockusch, Carl G., Jr.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
Given an (undecidable) elementary theory of a computability-theoretic structure, it is natural to ask how much of the theory is decidable. An AE-sentence is a sentence in prenex normal form with all universal quantifiers preceding all existential quantifiers, and the AE-theory of a structure is the set of all AE-sentences true in the structure. In Chapter 3 we show that the AE-theory of ( LP01 , ∩, ∪, 0, 1) is decidable. In Chapter 4 we show that the AE-theories of ( LP01 , ∩, ∪, 0, 1) and ( LP01 * , ∩, ∪, 0, 1) are different and provide a decision procedure for the AE-theory of ( LP01 * , ∩, ∪, 0, 1).
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