.

0 (hodnocen0 x )

BK

Dordrecht : Kluwer Academic Publishers, 2000

ix,231 s.

ISBN 0-7923-6009-5 (váz.)

Trends in logic : studia logica library

Obsahuje úvod, rejstřík

Bibliografie: s. 203-224

Algebra - logika - učebnice vysokošk.

000003170

Contents // Introduction 1 // 1 Basic notions 7 // 1.1 MV-algebras... 7 // 1.2 Homomorphisms and ideals ...12 // 1.3 Subdirect representation theorem...19 // 1.4 MV-equations...20 // 1.5 Boolean algebras...24 // 1.6 MV-chains...27 // 1.7 Bibliographical remarks ...29 // 2 Chang completeness theorem 31 // 2.1 The functor ?...31 // 2.2 Good sequences...34 // 2.3 The partially ordered monoid Ma...37 // 2.4 Chang’s Ł-group Ga...40 // 2.5 Chang completeness theorem...43 // 2.6 Bibliographical remarks ...49 // 3 Free MV-algebras 51 // 3.1 McNaughton functions...51 // 3.2 The one-dimensional case...56 // 3.3 Decomposing McNaughton functions...62 // 3.4 Ideals in free MV-algebras...64 // 3.5 Simple MV-algebras ... 70 // 3.6 Semisimple MV-algebras...72 // 3.7 Bibliographical remarks ...75 // vii // CONTENTS // viii // 4 Lukasiewicz oo-valued calculus 77 // 4.1 Many-valued propositional calculi...78 // 4.2 Wajsberg algebras...82 // 4.3 Provability...87 // 4.4 Lindenbaum algebra...92 // 4.5 All tautologies me provable ...94 // 4.6 Syntactic and semantic consequence...97 // 4.7 Bibliographical remarks ...101 // 5 Ulam’s game 103 // 5.1 Questions and answers...103 // 5.2 Dynamics of states of knowledge...104 // 5.3 Operations on states of knowledge...107 // 5.4 Bibliographical remarks ...109 // 6 Lattice-theoretical properties 111 // 6.1 Minimal prime ideals...112 // 6.2 Stonean ideals and archimedean elements...115 // 6.3 Hyperarchimedean algebras...116 // 6.4 Direct products...121

6.5 Boolean products of MV-algebras...124 // 6.6 Completeness...129 // 6.7 Atoms and Pseudocomplements...132 // 6.8 Complete distributivity...134 // 6.9 Bibliographical remarks ...137 // 7 MV-algebras and  -groups 139 // 7.1 Inverting the functor ?...139 // 7.2 Applications...146 // 7.3 The radical...150 // 7.4 Perfect MV-algebras...151 // 7.5 Bibliographical remarks ...156 // 8 Varieties of MV-algebras 157 // 8.1 Basic definitions...157 // 8.2 Varieties from simple algebras...160 // 8.3 MV-chains of finite rank...161 // CONTENTS // ix // 8.4 Komori’s classification...167 // 8.5 Varieties generated by a finite chain...171 // 8.6 The cardinality of Free?...173 // 8.7 Bibliographical remarks ...177 // 9 Advanced topics 179 // 9.1 McNaughton’s theorem...180 // 9.2 Nonsingular fans and normal forms...185 // 9.3 Complexity of the tautology problem...187 // 9.4 MV-algebras and AF C*-algebras...191 // 9.5 Di Nola’s representation theorem...193 // 9.6 Bibliographical remarks ...194 // 10 Further Readings 197 // 10.1 More than two truth values...197 // 10.2 Current Research Topics...199 // 10.2.1 Product...199 // 10.2.2 States, Observables, Probability, Partitions ... 200 // 10.2.3 Deduction...201 // 10.2.4 Further constructions...201 // Bibliography 203 // Index // 225