Relation Algebras
Springer International Publishing
978-3-319-68580-9 (ISBN)
This set charts relation algebras from novice to expert level. The first volume, Introduction to Relation Algebras, offers a comprehensive grounding for readers new to the topic. The second, Advanced Topics in Relation Algebras, build on this foundation and advances the reader into the deeper mathematical results of the past few decades. Such material offers an ideal preparation for research in relation algebras and Boolean algebras with operators.
Note thatthe second volume contains numerous, essential references to the first. Readers of the advanced material are encouraged to purchase the pair as a set, as access to the first book is necessary to make use of the second.
Steven Givant is a Professor of Mathematics and Computer Science at Mills College, California. As a long-term collaborator of Alfred Tarski-one of the great logicians-Givant has been involved first-hand in the development of the field of relation algebras since the 1970s. His previous books include Duality Theories for Boolean Algebras with Operators (Springer, 2014), Introduction to Boolean Algebras, with Paul Halmos (Springer, 2009), Logic as Algebra, with Paul Halmos (MAA, 1998), and A Formalization of Set Theory without Variables, with Alfred Tarski (AMS, 1987). He was also coeditor, with Ralph McKenzie, of Alfred Tarski's Collected Papers: Vol 1-4 (Birkhäuser, 1986).
Introduction to Relation Algebras.- Preface.- Introduction.- 1. The calculus of relations.- 2. Relation algebras.- 3. Examples of relation algebras.- 4. Arithmetic.- 5. Special elements.- 6. Subalgebras.- 7. Homomorphisms.- 8. Ideals and quotients.- 9. Simple algebras.- 10. Relativizations.- 11. Direct products.- 12. Subdirect products.- 13. Minimal relation algebras.- References.- Index.- Advanced Topics in Relation Algebras.- Preface.- Introduction.- 14. Canonical Extensions.- 15. Completions.- 16. Representations.- 17. Representation Theorems.- 18. Varieties of Relation Algebras.- 19. Atom Structures.- Epilogue.- References.- Index.
| Erscheint lt. Verlag | 14.9.2017 |
|---|---|
| Zusatzinfo | Approx. 1230 p. 2 volume-set. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
| Mathematik / Informatik ► Mathematik ► Algebra | |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| Schlagworte | Alfred Tarski relation algebras • Algebra • Arithmetic of relation algebras • Atom structures • Canonical extensions • Constructing new relation algebras • Elementary theory of binary relations • Equational language of relation algebras • General algebraic systems • homomorphisms • Mathematical Foundations • Mathematical Logic • Mathematical Logic and Foundations • Mathematics • mathematics and statistics • Relation algebras • representations • Special elements in relation algebras • Steven Givant relation algebras • Subalgebras of relation algebras • Varieties of relation algebras |
| ISBN-10 | 3-319-68580-5 / 3319685805 |
| ISBN-13 | 978-3-319-68580-9 / 9783319685809 |
| Zustand | Neuware |
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