Universal algebraic logic: dedicated to the unity of science

The three main themes of this book are (i) universal logic and the question of what logic is, (ii) universal algebraic logic and duality theories between the world of logics and the world of algebra, and (iii) algebraic logic proper including algebras of relations of various ranks, Tarski's cylindric algebras,relation algebras, Halmos' polyadic algebras and other kinds of algebras of logic. Besides Tarskian algebraizations of logics, category theoretical perspectives are also touched upon. Following the Tarskian tradition, besides the connections between logic and algebra, related logical connections with geometry and eventually spacetime geometry leading up to relativity are also part of the perspective of the book. An introductory chapter contains the necessary algebraic basics, this can be used in its own right as a quick introduction to universal algebra. Introduction to algebraic basics INDICE: 1. Introduction.- 2. Notation, elementary concepts.- 3. Basics from universal algebra.- 4. General framework for studying logics.- 5. Bridge between the world of logics and the world of algebras.- 6. Generalizations.- 7. Further equivalence results (definability, interpolation, omitting types).- 8. New kinds of logics 9. The guarded fragment and its finite variable hierarchy.- 10. Distinguished algebras of logic.- 11. Applications of the algebraic results to logic (via our bridge).- 12. Connections with set theory and foundational thinking.- 13. Connections with abstract model theory.- 14. Extending the bridge to including logic of spacetime, connections with relativity.- 15. On the problems in the books Henkin-Monk-Tarski: Cylindric Algebras Parts I, II andHenkin-Monk-Tarski-Andreka-Nemeti.- Some further problems.

• ISBN: 978-3-7643-8505-7
• Editorial: Birkhauser
• Encuadernacion: Rústica
• Páginas: 260
• Fecha Publicación: 01/01/2008
• Nº Volúmenes: 1
• Idioma: Inglés