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Umfang: 1 online resource (421 pages)

ISBN: 1-283-52559-3 , 9786613838049 , 0-08-095488-X

Serie: Studies in logic and the foundations of mathematics

Anmerkung: Front Cover; An Algebraic Approach to Non-Classical Logics; Copyright Page; Contents; PART ONE: IMPLICATIVE ALGEBRAS AND LATTICES; Chapter I. Preliminary set-theoretical, topological and algebraic notions; Introduction; 1. Sets, mappings; 2. Topological spaces; 3. Ordered sets and quasi-ordered sets; 4. Abstract algebras; 5. Exercises; Chapter II. Implicative algebras; Introduction; 1. Definition and elementary properties; 2. Positive implication algebras; 3. Implicative filters in positive implication algebras; 4. Representation theorem for positive implication algebras , 5. Implication algebras; 6. Implicative filters in implication algebras; 7. Representation theorem for implication algebras; 8. Exercises; Chapter III. Distributive lattices and quasi-Boolean algebras; Introduction; 1. Lattices; 2. Distributive lattices; 3. Quasi-Boolean algebras; 4. Exercises; Chapter IV. Relatively pseudo-complemented lattices, contrapositionally complemented lattices, semi-complemented lattices and pseudo-Boolean algebras; Introduction; 1. Relatively pseudo-complemented lattices; 2. Filters in relatively pseudo-complemented lattices , 3. Representation theorem for relatively pseudo-complemented lattices; 4. Contrapositionally complemented lattices; 5. Semi-complemented lattices; 6. Pseudo-Boolean algebras; 7. Exercises; Chapter V. Quasi-pseudo-Boolean algebras; Introduction; 1. Definition and elementary properties; 2. Equational definability of quasi-pseudo-Boolean algebras; 3. Examples of quasi-pseudo-Boolean algebras; 4. Filters in quasi-pseudo-Boolean algebras; 5. Representation theorem for quasi-pseudo-Boolean algebras; 6. Exercises; Chapter VI. Boolean algebras and topological Boolean algebras; Introduction , 1. Definition and elementary properties of Boolean algebras; 2. Subalgebras of Boolean algebras; 3. Filters and implicative filters in Boolean algebras; 4. Representation theorem for Boolean algebras; 5. Topological Boolean algebras; 6. I-filters in topological Boolean algebras; 7. Representation theorem for topological Boolean algebras; 8. Strongly compact topological spaces; 9. A lemma on imbedding for topological Boolean algebras , 10. Connections between topological Boolean algebras, pseudo-Boolean algebras, relatively pseudo-complemented lattices, contrapositionally complemented lattices and semi-complemented lattices; 11. Lemmas on imbeddings for pseudo-Boolean algebras, relatively pseudo-complemented lattices, contrapositionally complemented lattices and semi-complemented lattices.; 12. Exercises; Chapter VII. Post algebras; Introduction; 1. Definition and elementary properties; 2. Examples of Post algebras; 3. Filters and D-filters in Post algebras; 4. Post homomorphisms; 5. Post fields of sets; 6. Representation theorem for Post algebras , English

Weitere Ausg.: ISBN 0-7204-2264-7

Sprache: Englisch