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  1. Demuth’s path to randomness.Antonín Kučera, André Nies & Christopher P. Porter - 2015 - Bulletin of Symbolic Logic 21 (3):270-305.
    Osvald Demuth studied constructive analysis from the viewpoint of the Russian school of constructive mathematics. In the course of his work he introduced various notions of effective null set which, when phrased in classical language, yield a number of major algorithmic randomness notions. In addition, he proved several results connecting constructive analysis and randomness that were rediscovered only much later.In this paper, we trace the path that took Demuth from his constructivist roots to his deep and innovative work on the (...)
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  • When series of computable functions with varying domains are computable.Iraj Kalantari & Larry Welch - 2013 - Mathematical Logic Quarterly 59 (6):471-493.
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  • On Turing degrees of points in computable topology.Iraj Kalantari & Larry Welch - 2008 - Mathematical Logic Quarterly 54 (5):470-482.
    This paper continues our study of computable point-free topological spaces and the metamathematical points in them. For us, a point is the intersection of a sequence of basic open sets with compact and nested closures. We call such a sequence a sharp filter. A function fF from points to points is generated by a function F from basic open sets to basic open sets such that sharp filters map to sharp filters. We restrict our study to functions that have at (...)
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  • On degree-preserving homeomorphisms between trees in computable topology.Iraj Kalantari & Larry Welch - 2008 - Archive for Mathematical Logic 46 (7-8):679-693.
    In this paper we first give a variant of a theorem of Jockusch–Lewis– Remmel on existence of a computable, degree-preserving homeomorphism between a bounded strong ${\Pi^0_2}$ class and a bounded ${\Pi^0_1}$ class in 2 ω . Namely, we show that for mathematically common and interesting topological spaces, such as computably presented ${\mathbb{R}^n}$ , we can obtain a similar result where the homeomorphism is in fact the identity mapping. Second, we apply this finding to give a new, priority-free proof of existence (...)
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  • Density and Baire category in recursive topology.Iraj Kalantari & Larry Welch - 2004 - Mathematical Logic Quarterly 50 (4-5):381-391.
    We develop the concepts of recursively nowhere dense sets and sets that are recursively of first category and study closed sets of points in light of Baire's Category Theorem. Our theorems are primarily concerned with exdomains of recursive quantum functions and hence with avoidable points . An avoidance function is a recursive function which can be used to expel avoidable points from domains of recursive quantum functions. We define an avoidable set of points to be an arbitrary subset of the (...)
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  • A blend of methods of recursion theory and topology: A Π1 0 tree of shadow points. [REVIEW]Iraj Kalantari & Larry Welch - 2004 - Archive for Mathematical Logic 43 (8):991-1008.
    This paper is a sequel to our [7]. In that paper we constructed a Π1 0 tree of avoidable points. Here we construct a Π1 0 tree of shadow points. This tree is a tree of sharp filters, where a sharp filter is a nested sequence of basic open sets converging to a point. In the construction we assign to each basic open set on the tree an address in 2<ω. One interesting fact is that while our Π1 0 tree (...)
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  • Closed choice and a uniform low basis theorem.Vasco Brattka, Matthew de Brecht & Arno Pauly - 2012 - Annals of Pure and Applied Logic 163 (8):986-1008.
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