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Relational quantifiers

Seria
Rozprawy Matematyczne tom/nr w serii: 347 wydano: 1995
Zawartość
Warianty tytułu
Abstrakty
EN
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
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
  • Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
Bibliografia
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  • [3] G. A. Broesterhuizen, Structures for a logic with additional generalized quantifier, Colloq. Math. 33 (1975), 1-12.
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  • [11] V. Harizanov, Łoś theorem for ultraproducts of models with monotone quantifiers, J. Symbolic Logic 48 (1983), 1212 (abstract).
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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
Identyfikatory
ISSN
0012-3862
Kolekcja
DML-PL
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