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Recursive Boolean algebras with recursive atoms

Jeffrey B. Remmel

Journal of Symbolic Logic 46 (3):595-616 (1981)

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Computable Heyting Algebras with Distinguished Atoms and Coatoms.Nikolay Bazhenov - 2023 - Journal of Logic, Language and Information 32 (1):3-18.details The paper studies Heyting algebras within the framework of computable structure theory. We prove that the class _K_ containing all Heyting algebras with distinguished atoms and coatoms is complete in the sense of the work of Hirschfeldt et al. (Ann Pure Appl Logic 115(1-3):71-113, 2002). This shows that the class _K_ is rich from the computability-theoretic point of view: for example, every possible degree spectrum can be realized by a countable structure from _K_. In addition, there is no simple syntactic (...) Download Export citation Bookmark
Recursively rigid Boolean algebras.Jeffrey B. Remmel - 1987 - Annals of Pure and Applied Logic 36:39-52.details Download Export citation Bookmark 1 citation
Recursive linear orders with recursive successivities.Michael Moses - 1984 - Annals of Pure and Applied Logic 27 (3):253-264.details A successivity in a linear order is a pair of elements with no other elements between them. A recursive linear order with recursive successivities U is recursively categorical if every recursive linear order with recursive successivities isomorphic to U is in fact recursively isomorphic to U . We characterize those recursive linear orders with recursive successivities that are recursively categorical as precisely those with order type k 1 + g 1 + k 2 + g 2 +…+ g n -1 (...) Download Export citation Bookmark 9 citations
Recursive unary algebras and trees.Bakhadyr Khoussainov - 1994 - Annals of Pure and Applied Logic 67 (1-3):213-268.details A unary algebra is an algebraic system A = , where ƒ 0 ,…,ƒ n are unary operations on A and n ∈ ω. In the paper we develop the theory of effective unary algebras. We investigate well-known questions of constructive model theory with respect to the class of unary algebras. In the paper we construct unary algebras with a finite number of recursive isomorphism types. We give the notions of program, uniform, and algebraic dimensions of models, and then we (...) Download Export citation Bookmark 1 citation
Decidable Boolean algebras of low level.S. S. Goncharov - 1998 - Annals of Pure and Applied Logic 94 (1-3):75-95.details We will study the question about decidability for Boolean algebras with first elementary characteristic one. The main problem is sufficient conditions for decidability of Boolean algebras with recursive representation for extended signature by definable predicates. We will use the base definitions on recursive and constructive models from [2, 4–6, 10, 11] but on Boolean algebras from [1, 8]. Download Export citation Bookmark
Every recursive boolean algebra is isomorphic to one with incomplete atoms.Rod Downey - 1993 - Annals of Pure and Applied Logic 60 (3):193-206.details The theorem of the title is proven, solving an old question of Remmel. The method of proof uses an algebraic technique of Remmel-Vaught combined with a complex tree of strategies argument where the true path is needed to figure out the final isomorphism. Download Export citation Bookmark 6 citations

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