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Umfang: 1 online resource (513 p.)

ISBN: 1-283-52553-4 , 9786613837981 , 0-08-095478-2

Serie: Studies in logic and the foundations of mathematics ; v. 66

Inhalt: Provability, Computability and Reflection

Anmerkung: Description based upon print version of record. , 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 algebrasChapter 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 t5. 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 algebrasChapter 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 types1. 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 , English

Weitere Ausg.: ISBN 0-7204-2266-3

Sprache: Englisch