Countable Boolean Algebras And Decidability
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Countable Boolean Algebras and Decidability
Author: Sergey Goncharov
language: en
Publisher: Springer Science & Business Media
Release Date: 1997-01-31
This book describes the latest Russian research covering the structure and algorithmic properties of Boolean algebras from the algebraic and model-theoretic points of view. A significantly revised version of the author's Countable Boolean Algebras (Nauka, Novosibirsk, 1989), the text presents new results as well as a selection of open questions on Boolean algebras. Other current features include discussions of the Kottonen algebras in enrichments by ideals and automorphisms, and the properties of the automorphism groups.
Decidability and Boolean Representations
Author: Stanley Burris
language: en
Publisher: American Mathematical Soc.
Release Date: 1981
In part I we address the question: which varieties have a decidable first order theory? We confine our attention to varieties whose algebras have modular congruence lattices (i.e., modular varieties), and focus primarily on locally finite varieties, although near the end of the paper Zamjatin's description of all decidable varieties of groups and rings, and offer a new proof of it. In part II, we show that if a variety admits such sheaf representations using only finitely many stalks, all of which are finite, then the variety can be decomposed in the product of a discriminator variety and an abelian variety. We continue this investigation by looking at well-known specializations of the sheaf construction, namely Boolean powers and sub-Boolean powers, giving special emphasis to quasi-primal algebras A, such that the sub-Boolean powers of A form a variety (this extends the work of Arens and Kaplansky on finite fields).
Programs, Proofs, Processes
Author: Fernando Ferreira
language: en
Publisher: Springer Science & Business Media
Release Date: 2010-06-17
This book constitutes the refereed proceedings of the 6th Conference on Computability in Europe, CiE 2010, held in Ponta Delgada, Azores, Portugal, in June/July 2010. The 28 revised papers presented together with 20 invited lectures were carefully reviewed and selected from 90 submissions. The papers address not only the more established lines of research of computational complexity and the interplay between proofs and computation, but also novel views that rely on physical and biological processes and models to find new ways of tackling computations and improving their efficiency.