The Metamathematics of Algebraic Systems, Collected Papers: 1936-1967

Name: The Metamathematics of Algebraic Systems, Collected Papers: 1936-1967
Brand: Elsevier
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A. I. Mal'tsev Lev D. Beklemishev(Autor*in)

Elsevier (Verlag)

Erschienen am 14. Mai 2014

513 Seiten

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Front Cover
The Metamathematics of Algebraic Systems
Copyright Page
Contents
Translator's foreword
Biographical note
Chapter 1. Investigations in the realm of mathematical logic
Chapter 2. A general method for obtaining local theorems in group theory
Chapter 3. Representations of models
Chapter 4. Quasiprimitive classes of abstract algebras
Chapter 5. Subdirect products of models
Chapter 6. Derived operations and predicates
Chapter 7. Classes of models with an operation of generation
Chapter 8. Defining relations in categories
Chapter 9. The structural characterization of certain classes of algebras
Chapter 10. Certain classes of models
Chapter 11. Model correspondences
Introduction
§1. Multibase models
§2. Fundamental properties of projective correspondences
§3. Quasiuniversal subclasses
Chapter 12. Regular products of models
Introduction
§1. Splitting correspondences
§2. Regular products
Chapter 13. Small models
Chapter 14. Free solvable groups
Chapter 15. A correspondence between rings and groups
§1. The direct mapping
§2. Groups with distinguished elements
§3. The inverse mapping
§4. The reciprocity of the correspondences s and t
§5. Some special cases
§6. Reductions and interpretations of classes of models
§7. The undecidability of sundry classes of metabelian groups
§8. Nilpotent groups
Chapter 16. The undecidability of the elementary theories of certain fields
§1. The field of rational functions
§2. Fields of formal power series
Chapter 17. A remark concerning "The undecidability of the elementary theories of certain fields" [XVI]
Chapter 18. Constructive algebras. I
Introduction
§1. Algebraic systems
§2. Numbered sets
§3. Numbered algebraic systems
§4. Finitely generated algebras
Chapter 19. The undecidability of the elementary theory of finite groups
Chapter 20. Elementary properties of linear groups
Introduction
§1. The elementary nature of the Segre characteristic
§2. Elementary (arithmetic) types of linear and projective groups
Chapter 21. The effective inseparability of the set of valid sentences from the set of finitely refutable sentences in several elementary theories
Chapter 22. Closely related models and recursively perfect algebras
§1. Closely related models
§2. Recursively perfect algebras
§3. Linear groups
Chapter 23. Axiomatizable classes of locally free algebras of various types
§1. Locally absolutely free algebras
§2. Ordered groupoids
§3. G -algebras
§4. Special formulas
§5 . Standard formulas
§6. The reduction of negations of standard formulas
§7. The reduction of closed formulas
Chapter 24. Recursive abelian groups
Chapter 25. Sets with complete numberings
§1. Complete numberings
§2. Isomorphism. Factor numberings
§3. Enumerable families of elements
§4. Completely numbered sets whose every family of nonspecial elements is totally enumerable
§5. Universal series of sets
§6. Totally enumerable families of partial recursive functions
§7. Projective families of functions. Computable numberings
§8. Quasiordered families
§9. Intrinsically productive families
Chapter 26. Problems in the theory of classes of models
Introduction
§1. Fundamental concepts
§2. Axiomatizable classes of models
§3. Some special axiomatizable classes
§4. Ultraproducts
§5. A few second-order classes of models
Chapter 27. Toward a theory of computable families of objects
§1. principal and complete numberings
§2. The a-order and a-topology
§3. Normal and subnormal numberings
§4. Effectively principal numberings
§5. Standard families and precomplete numberings
§6. Special and subspecial numberings
§7. Totally enumerable families
Chapter 28. Positive and negative numberings
Chapter 29. Identical relations in varieties of quasigroups
§1. The problem of identical relations
§2. Algebras with unary operations
§3. Partial quasigroups
§4. Varieties of quasigroups
Chapter 30. Iterative algebras and Post varieties
§1. Iterative algebras
§2. Iterative algebras of partial functions
§3. Congruences on pi and Eliw
§4. Automorphisms
§5. Representations of iterative algebras
§6. Post variables
§7. Selector representations of pre-iterative algebras
§8. Subalgebras
Chapter 31. A few remarks on quasivarieties of algebraic systems
§1. Identities and quasidentities
§2. Quasivarieties of algebraic systems
Chapter 32. Multiplication of classes of algebraic systems
§1. The basic definition
§2. Products and axiomatizable classes
§3. Multiplication in special classes of systems
§4. Additional observations
Chapter 33. Universally axiomatizable subclasses of locally finite classes of models
§1. Conditions for universal axiomatizability
§2. Independent axiomatizability
§3. Graphs of finite degree
§4. Uniformly locally finite classes
Cxapter 34. Problems on the border between algebra and logic
§1. The algorithmic nature of theories
§2. Varieties and quasivarieties
Bibliography
Part I. The articles translated in this collection
Part II. Previous English translations
Part III. Other works of A.I. Mal'cev
Part IV. Reviews cited in editor's notes
Part V. Obituaries with bibliographies
Part VI. General references
Topic table
Index

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