Tran, Ying-Ying2018-10-232018-10-232018-05-30Tran_cornellgrad_0058F_10785http://dissertations.umi.com/cornellgrad:10785bibid: 10489589https://hdl.handle.net/1813/59504We 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.en-USAttribution-ShareAlike 4.0 InternationalStone dualityuniversal-homogeneousLogicboolean algebracomputably enumerabledissertation or thesishttps://doi.org/10.7298/X4Z60M82