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Some ComputabilityTheoretical Aspects of Reals and Randomness
, 2001
"... We study computably enumerable reals (i.e. their left cut is computably enumerable) in terms of their spectra of representations and presentations. Then we study such objects in terms of algorithmic randomness, culminating in some recent work of the author with Hirschfeldt, Laforte, and Nies conce ..."
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Cited by 21 (7 self)
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We study computably enumerable reals (i.e. their left cut is computably enumerable) in terms of their spectra of representations and presentations. Then we study such objects in terms of algorithmic randomness, culminating in some recent work of the author with Hirschfeldt, Laforte, and Nies concerning methods of calibrating randomness.
Effective presentability of Boolean algebras of CantorBendixson rank 1
 Journal of Symbolic Logic
, 1999
"... We show that there is a computable Boolean algebra B and a computably enumerable ideal I of B such that the quotient algebra B/I is of CantorBendixson rank 1 and is not isomorphic to any computable Boolean algebra. This extends a result of L. Feiner and is deduced from Feiner's result even tho ..."
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Cited by 6 (6 self)
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We show that there is a computable Boolean algebra B and a computably enumerable ideal I of B such that the quotient algebra B/I is of CantorBendixson rank 1 and is not isomorphic to any computable Boolean algebra. This extends a result of L. Feiner and is deduced from Feiner's result even though Feiner's construction yields a Boolean algebra of infinite CantorBendixson rank.
Computable Kripke Models and Intermediate Logics
, 1998
"... We introduce e#ectiveness considerations into model theory of intuitionistic logic. We investigate e#ectiveness of completeness #by Kripke# results for intermediate logics such as for example, intuitionistic logic, classical logic, constant domain logic, directed frames logic, Dummett's log ..."
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We introduce e#ectiveness considerations into model theory of intuitionistic logic. We investigate e#ectiveness of completeness #by Kripke# results for intermediate logics such as for example, intuitionistic logic, classical logic, constant domain logic, directed frames logic, Dummett's logic, etc. 1 Motivation The development of computable #equivalently, recursive# function theory made it possible to investigate the computational aspects of many mathematical notions and constructions within the context of classical mathematics. # The work of Khoussainov and Ishihara is supported by Japan Advanced Institute of Science and Technology #JAIST#. Khoussainovacknowledges the support of the University of Auckland Research Committee. Nerode is partially supported byARO under MURI grantDAAH 049610341, Integrated ApproachtoIntelligent Systems. 1 In the 1930's Kleene and Church investigated computabilityonthe integers and in well#ordered sets and invented the notion of recursive ordina...