Relational quantifiers

Krynicki Michał

GDML_Books, (1995), p.

Résumé

CONTENTS  Introduction.................................................................................5 1. Algebras of monotone quantifiers.............................................7  1.1. Family of monotone quantifiers............................................7  1.2. Lattice of monotone quantifiers............................................8  1.3. Other operations in M(κ)......................................................9 2. Algebras of relational quantifiers............................................11  2.1. Basic properties of the family of relational quantifiers........11  2.2. Relations and quantifiers...................................................13  2.3. Lattices of relational quantifiers.........................................15  2.4. Other operations in R(κ)....................................................17 3. Logics with relational quantifiers............................................18  3.1. Structures with relational quantifiers..................................18  3.2. Completeness theorem......................................................19  3.3. Some simple consequences...............................................20 4. Model theory of relational quantifiers.....................................21  4.1. Basic notions......................................................................21  4.2. Substructure relations and preservation therems..............23  4.3. The chain property.............................................................27  4.4. Product operations............................................................29 5. Classes of relations and their logics......................................33  5.1. Logics determined by classes of relations.........................33  5.2. Classes of relations vs. sets of sentences.........................36  5.3. The Galois connection.......................................................38  5.4. The lattice of closed classes..............................................40  5.5. Further properties..............................................................44  5.6. Some open questions........................................................45  References...............................................................................46

1991 Mathematics Subject Classification: Primary 03C80; Secondary 06A15, 06B99.

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EUDML-ID : urn:eudml:doc:275825