Countable Boolean Algebras and DecidabilitySpringer Science & Business Media, 31 ene 1997 - 330 páginas 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. |
Índice
Algebraic Properties of Boolean Algebras | 1 |
12 Definitions and the Simplest Properties of Boolean Algebras | 15 |
13 Ideals and Quotient Algebras of Boolean Algebras | 26 |
14 The Stone Theorem on Representations of Boolean Algebras | 39 |
15 The Vaught Criterion | 44 |
16 Linearly Ordered Generating Sets | 53 |
17 Generating Trees | 59 |
18 Ershov Algebras and The Isomorphism Problem | 71 |
26 Restricted Theories of Boolean Algebras | 139 |
Constructive Boolean Algebras | 149 |
31 Basic Notions of the Theory of Algorithms and Constructive Models | 150 |
32 Constructibility in Linear Orders and Boolean Algebras | 174 |
33 Trees Generating Constructive Boolean Algebras | 180 |
34 Decidable Boolean Algebras | 190 |
35 Restricted Fragments of the Theory of Boolean Algebras and Decidable Algebras | 214 |
36 Algorithmic Dimension of Boolean Algebras | 249 |
Elementary Classification of Boolean Algebras | 91 |
22 Definable ErshovTarski Ideals and Elementary Characteristics of Boolean Algebras | 108 |
23 Countably Saturated Boolean Algebras and Elementary Classification | 114 |
24 ModelComplete Theories of Boolean Algebras | 127 |
25 Consistent Complete Theories of Boolean Algebras | 132 |
37 Algorithmic Properties of Subalgebras and Quotient Algebras of Constructive Boolean Algebras | 261 |
38 Automorphisms of Countable Boolean Algebras | 290 |
303 | |
315 | |
Términos y frases comunes
3-formula A₁ algebraic system algorithmic assume atomic Boolean algebra atomic element atomless Boolean algebra atomless element automorphism B-constructive B-recursive b₁ belongs Boolean algebra BL Boolean lattice called ch₁ ch₁(a ch₁(b computable sequence Consequently consider constructive Boolean algebra constructive models constructivization Corollary countable Boolean algebra d₁ decidable define denoted dense Boolean algebra elementarily equivalent elementary characteristic elementary embedding elementary extension epimorphism equivalent Ershov algebra finite number following conditions hold Frechét ideal Gödel number greatest element homogeneous homogeneous model homomorphism infinite isomorphic embedding least element Lemma linear order mapping model-complete natural numbers number of atoms number of elements obtain ordered set ordinal partition PROOF properties Proposition Prove quotient algebra recursive Boolean algebra recursive function recursive set recursively enumerable recursively isomorphic satisfies saturated model set of atoms step subalgebra subset superatomic superatomic Boolean algebra Theorem tree ultrafilter variables
Referencias a este libro
Computability Theory and Its Applications: Current Trends and Open Problems ... Peter Cholak No hay ninguna vista previa disponible - 2000 |