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Warianty tytułu
Abstrakty
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
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
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
347
Liczba stron
47
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCXLVII
Daty
wydano
1995
otrzymano
1992-11-30
poprawiono
1994-11-29
Twórcy
autor
- Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
Bibliografia
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Języki publikacji
EN |
Uwagi
1991 Mathematics Subject Classification: Primary 03C80; Secondary 06A15, 06B99.
Identyfikator YADDA
bwmeta1.element.zamlynska-69d8e752-9ee8-405e-8334-f617194efddd
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ISSN
0012-3862
Kolekcja
DML-PL
