Computably enumerable boolean algebras
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We study computably enumerable boolean algebras, focusing on Stone duality and universality phenomena. We show how classical Stone duality specializes to c.e. boolean algebras, giving a natural bijection between c.e. boolean algebras and $\Pi^0_1$ classes. We also give a new characterization of computably universal-homogeneous c.e. boolean algebras, which yields a more direct proof of the computable isomorphism between the Lindenbaum algebras of theories which satisfy the hypotheses of the second incompleteness theorem.
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2018-05-30
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Stone duality; universal-homogeneous; Logic; boolean algebra; computably enumerable
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Nerode, Anil
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Kress Gazit, Hadas
Shore, Richard A.
Shore, Richard A.
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Mathematics
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Ph. D., Mathematics
Degree Level
Doctor of Philosophy
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Government Document
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Attribution-ShareAlike 4.0 International
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dissertation or thesis