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Borel liftings of Borel sets : some decidable and undecidable statements / / Gabriel Debs, Jean Saint Raymond
| Borel liftings of Borel sets : some decidable and undecidable statements / / Gabriel Debs, Jean Saint Raymond |
| Autore | Debs Gabriel <1952-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2007 |
| Descrizione fisica | 1 online resource (134 p.) |
| Disciplina | 511.322 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Borel sets
Descriptive set theory Constructibility (Set theory) |
| ISBN | 1-4704-0480-X |
| Classificazione | 31.10 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Introduction ""; ""0.1. Descriptive classes: ""; ""0.2. An elementary topological problem: ""; ""0.3. Continuous and Borel liftings: ""; ""0.4. Main result ""; ""0.5. Application 1 ""; ""0.6. Application 2 ""; ""0.7. Application 3 ""; ""Chapter 1. A Tree Representation for Borel Sets ""; ""1.1. Trees ""; ""1.2. Distinguished subrelation ""; ""1.3. Canonical mapping of a distinguished subtree ""; ""1.4. Uniformly distinguished subtree ""; ""1.5. Tree products ""; ""1.6. Tree expansions and representations of Borel sets ""; ""1.7. Regular expansions and representations ""
""Chapter 2. A Double-Tree Representation for Borel Sets """"2.1. Double-trees ""; ""2.2. Double-tree characterization of â??[sup(0)][sub(2)] sets""; ""2.3. Double-tree characterization of D(â??[sup(0)][sub(2)]) sets""; ""2.4. Appendix : extension to Wadge classes""; ""Chapter 3. Two Applications of the Tree Representation""; ""3.1. Resolution of quasi-strategies""; ""3.2. Hurewicz type results""; ""3.3. A Borel separation result""; ""Chapter 4. Borel Liftings of Borel Sets""; ""4.1. Borel liftings of bounded rank""; ""4.2. Borel liftings of unbounded rank"" ""4.3. Solution to Ostrovsky's problem""""4.4. Borel liftings in coanalytic sets""; ""Chapter 5. More Consequences and Reverse Results""; ""5.1. Some boudedness principles""; ""5.2. Reverse results""; ""5.3. Conclusion""; ""5.4. Appendix: A Perfect Set Theorem for a Class of Equivalence Relations""; ""Chapter 6. Proof of The Main Result""; ""6.1. Sketch of the proof""; ""6.2. Labeling games with delay""; ""6.3. Proof of the basic case""; ""6.4. Proof of the general limit case""; ""6.5. Proof of the general successor case""; ""Bibliography""; ""Index"" |
| Record Nr. | UNINA-9910788744303321 |
Debs Gabriel <1952->
|
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| Providence, Rhode Island : , : American Mathematical Society, , 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Borel liftings of Borel sets : some decidable and undecidable statements / / Gabriel Debs, Jean Saint Raymond
| Borel liftings of Borel sets : some decidable and undecidable statements / / Gabriel Debs, Jean Saint Raymond |
| Autore | Debs Gabriel <1952-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2007 |
| Descrizione fisica | 1 online resource (134 p.) |
| Disciplina | 511.322 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Borel sets
Descriptive set theory Constructibility (Set theory) |
| ISBN | 1-4704-0480-X |
| Classificazione | 31.10 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Introduction ""; ""0.1. Descriptive classes: ""; ""0.2. An elementary topological problem: ""; ""0.3. Continuous and Borel liftings: ""; ""0.4. Main result ""; ""0.5. Application 1 ""; ""0.6. Application 2 ""; ""0.7. Application 3 ""; ""Chapter 1. A Tree Representation for Borel Sets ""; ""1.1. Trees ""; ""1.2. Distinguished subrelation ""; ""1.3. Canonical mapping of a distinguished subtree ""; ""1.4. Uniformly distinguished subtree ""; ""1.5. Tree products ""; ""1.6. Tree expansions and representations of Borel sets ""; ""1.7. Regular expansions and representations ""
""Chapter 2. A Double-Tree Representation for Borel Sets """"2.1. Double-trees ""; ""2.2. Double-tree characterization of â??[sup(0)][sub(2)] sets""; ""2.3. Double-tree characterization of D(â??[sup(0)][sub(2)]) sets""; ""2.4. Appendix : extension to Wadge classes""; ""Chapter 3. Two Applications of the Tree Representation""; ""3.1. Resolution of quasi-strategies""; ""3.2. Hurewicz type results""; ""3.3. A Borel separation result""; ""Chapter 4. Borel Liftings of Borel Sets""; ""4.1. Borel liftings of bounded rank""; ""4.2. Borel liftings of unbounded rank"" ""4.3. Solution to Ostrovsky's problem""""4.4. Borel liftings in coanalytic sets""; ""Chapter 5. More Consequences and Reverse Results""; ""5.1. Some boudedness principles""; ""5.2. Reverse results""; ""5.3. Conclusion""; ""5.4. Appendix: A Perfect Set Theorem for a Class of Equivalence Relations""; ""Chapter 6. Proof of The Main Result""; ""6.1. Sketch of the proof""; ""6.2. Labeling games with delay""; ""6.3. Proof of the basic case""; ""6.4. Proof of the general limit case""; ""6.5. Proof of the general successor case""; ""Bibliography""; ""Index"" |
| Record Nr. | UNINA-9910829174403321 |
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Debs Gabriel <1952->
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| Providence, Rhode Island : , : American Mathematical Society, , 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fuzzy neural network theory and application [[electronic resource] /] / Puyin Liu, Hongxing Li
| Fuzzy neural network theory and application [[electronic resource] /] / Puyin Liu, Hongxing Li |
| Autore | Liu Puyin |
| Pubbl/distr/stampa | River Edge, NJ, : World Scientific, c2004 |
| Descrizione fisica | 1 online resource (395 p.) |
| Disciplina | 006.32 |
| Altri autori (Persone) | LiHong-Xing <1953-> |
| Collana | Series in machine perception and artificial intelligence |
| Soggetto topico |
Neural networks (Computer science)
Fuzzy systems |
| ISBN |
1-281-93438-0
9786611934385 981-279-421-2 |
| Classificazione |
54.72
31.10 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents ; Foreword ; Preface ; Chapter I Introduction ; S1.1 Classification of fuzzy neural networks ; S1.2 Fuzzy neural networks with fuzzy operators ; S1.3 Puzzified neural networks ; 1.3.1 Learning algorithm for regular FNN's ; 1.3.2 Universal approximation of regular FNN's
S1.4 Fuzzy systems and fuzzy inference networks 1.4.1 Fuzzy systems ; 1.4.2 Fuzzy inference networks ; S1.5 Fuzzy techniques in image restoration ; 1.5.1 Crisp nonlinear filters ; 1.5.2 Fuzzy filters ; S1.6 Notations and preliminaries ; S1.7 Outline of the topics of the chapters References Chapter II Fuzzy Neural Networks for Storing and Classifying ; S2.1 Two layer max-min fuzzy associative memory ; 2.1.1 FAM with threshold ; 2.1.2 Simulation example ; S2.2 Fuzzy 6-learning algorithm ; 2.2.1 FAM's based on 'V - /\' ; 2.2.2 FAM's based on 'V - *' S2.3 BP learning algorithm of FAM's 2.3.1 Two analytic functions ; 2.3.2 BP learning algorithm ; S2.4 Fuzzy ART and fuzzy ARTMAP ; 2.4.1 ART1 architecture ; 2.4.2 Fuzzy ART ; 2.4.3 Fuzzy ARTMAP ; 2.4.4 Real examples ; References Chapter III Fuzzy Associative Memory-Feedback Networks S3.1 Fuzzy Hopfield networks ; 3.1.1 Attractor and attractive basin ; 3.1.2 Learning algorithm based on fault-tolerance ; 3.1.3 Simulation example ; S3.2 Fuzzy Hopfield network with threshold ; 3.2.1 Attractor and stability 3.2.2 Analysis of fault-tolerance |
| Record Nr. | UNINA-9910782118803321 |
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Liu Puyin
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| River Edge, NJ, : World Scientific, c2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Residuated lattices [[electronic resource] ] : an algebraic glimpse at substructural logics / / Nikolaos Galatos ... [et al.]
| Residuated lattices [[electronic resource] ] : an algebraic glimpse at substructural logics / / Nikolaos Galatos ... [et al.] |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Amsterdam ; ; Boston, : Elsevier, 2007 |
| Descrizione fisica | 1 online resource (532 p.) |
| Disciplina | 511.33 |
| Altri autori (Persone) | GalatosNikolaos |
| Collana | Studies in logic and the foundations of mathematics |
| Soggetto topico |
Algebraic logic
Lattice theory |
| ISBN |
1-281-05106-3
9786611051068 0-08-048964-8 |
| Classificazione | 31.10 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Copyright Page; Table of Contents; Detailed Contents; List of Figures; List of Tables; Introduction; Chapter 1. Getting started; 1.1. First-order languages and semantics; 1.1.1. Preorders; 1.1.2. Posets; 1.1.3. Lattices; 1.1.4. Heyting algebras and Boolean algebras; 1.1.5. Semigroups, monoids and other groupoids; 1.2. Concepts from universal algebra; 1.2.1. Homomorphisms, subalgebras, substructures, direct products; 1.2.2. Congruences; 1.2.3. Free algebras; 1.2.4. More on Heyting and Boolean algebras; 1.2.5. Mal'cev conditions; 1.2.6. Ultraproducts and Jónsson's Lemma
1.2.7. Equational logic 1.2.8. Quasivarieties; 1.3. Logic; 1.3.1. Hilbert calculus for classical logic; 1.3.2. Gentzen's sequent calculus for classical logic; 1.3.3. Calculi for intuitionistic logic; 1.3.4. Provability in Hilbert and Gentzen calculi; 1.4. Logic and algebra; 1.4.1. Validity of formulas in algebras; 1.4.2. Lindenbaum-Tarski algebras; 1.4.3. Algebraization; 1.4.4. Superintuitionistic logics; 1.5. Cut elimination in sequent calculi; 1.5.1. Cut elimination; 1.5.2. Decidability and subformula property; 1.6. Consequence relations and matrices; 1.6.1. Consequence relations 1.6.2. Inference rules 1.6.3. Proofs and theorems; 1.6.4. Matrices; 1.6.5. Examples; 1.6.6. First-order and (quasi)equational logic; Exercises; Notes; Chapter 2. Substructural logics and residuated lattices; 2.1. Sequent calculi and substructural logics; 2.1.1. Structural rules; 2.1.2. Comma, fusion and implication; 2.1.3. Sequent calculus for the substructural logic FL; 2.1.4. Deducibility and substructural logics over FL; 2.2. Residuated lattices and FL-algebras; 2.3. Important subclasses of substructural logics; 2.3.1. Lambek calculus; 2.3.2. BCK logic and algebras; 2.3.3. Relevant logics 2.3.4. Linear logic 2.3.5. ukasiewicz logic and MV-algebras; 2.3.6. Fuzzy logics and triangular norms; 2.3.7. Superintuitionistic logics and Heyting algebras; 2.3.8. Minimal logic and Brouwerian algebras; 2.3.9. Fregean logics and equivalential algebras; 2.3.10. Overview of logics over FL; 2.4. Parametrized local deduction theorem; 2.5. Hilbert systems; 2.5.1. The systems HFLe and HFL; 2.5.2. Derivable rules; 2.5.3. Equality of two consequence relations; 2.6. Algebraization and deductive filters; 2.6.1. Algebraization; 2.6.2. Deductive filters; Exercises; Notes Chapter 3. Residuation and structure theory 3.1. Residuation theory and Galois connections; 3.1.1. Residuated pairs; 3.1.2. Galois connections; 3.1.3. Binary residuated maps; 3.2. Residuated structures; 3.3. Involutive residuated structures; 3.3.1. Involutive posets; 3.3.2. Involutive pogroupoids; 3.3.3. Involutive division posets; 3.3.4. Term equivalences; 3.3.5. Constants; 3.3.6. Dual algebras; 3.4. Further examples of residuated structures; 3.4.1. Boolean algebras and generalized Boolean algebras; 3.4.2. Partially ordered and lattice ordered groups 3.4.3. The negative cone of a residuated lattice |
| Record Nr. | UNINA-9910784596803321 |
| Amsterdam ; ; Boston, : Elsevier, 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||