| Description |
1 online resource (xiv, 311 pages) |
| Series |
Oxford logic guides ; 50 |
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Oxford logic guides ; 50.
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| Contents |
1 Basics; 1.1 Notation and basic definitions; 1.2 Skolem closures; 1.3 End extensions and cofinal extensions; 1.4 Coding bounded sets and classes; 1.5 Standard systems; 1.6 Types; 1.7 Blass-Gaifman and Ehrenfeucht lemmas; 1.8 Recursive saturation and arithmetic saturation; 1.9 Satisfaction classes and resplendency; 1.10 Cuts and gaps in recursively saturated models; 1.11 Truth definitions and restricted saturation; 1.12 Arithmetized Completeness Theorem; 1.13 Friedman's Embedding Theorem; 1.14 Exercises; 1.15 Remarks & References; 2 Extensions; 2.1 Simple extensions |
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2.1.1 Minimal extensions2.1.2 Superminimal extensions; 2.1.3 Greatest common initial segments; 2.2 The MacDowell-Specker Theorem; 2.2.1 Superminimal conservative extensions; 2.2.2 Rather classless models; 2.2.3 Ramsey's Theorem in ACA[sub(0)]; 2.3 Amalgamations; 2.4 Nonelementary extensions; 2.5 Exercises; 2.6 Remarks & References; 3 Minimal and Other Types; 3.1 Types related to indiscernibility; 3.1.1 Indiscernible types; 3.1.2 n-indiscernible types; 3.1.3 End-extensional types; 3.1.4 Rare types; 3.2 Minimal types; 3.2.1 Selective types; 3.2.2 Characterizing minimal types; 3.2.3 An example |
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3.3 Canonical extensions3.3.1 Products of types; 3.3.2 The automorphism group; 3.3.3 The substructure lattice; 3.4 Resolute types; 3.5 The Paris-Mills theorems; 3.6 Exercises; 3.7 Remarks & References; 4 Substructure Lattices; 4.1 Lattices; 4.2 Substructure lattices; 4.3 Finite distributive lattices, I; 4.4 Finite distributive lattices, II; 4.5 Finite lattices; 4.6 The pentagon lattice; 4.7 Infinite distributive lattices; 4.8 Exercises; 4.9 Remarks & References; 5 How to Control Types; 5.1 Solid bases and AH-sets; 5.1.1 Controlling indiscernibles and automorphisms; 5.1.2 AH-sets |
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5.1.3 The proof5.1.4 True arithmetic; 5.2 Omitting indiscernibles; 5.3 Hanf numbers; 5.4 The automorphism group; 5.5 Indiscernible generators; 5.6 Exercises; 5.7 Remarks & References; 6 Generics and Forcing; 6.1 Generics; 6.2 Forcing; 6.2.1 Definition; 6.2.2 n-Generics; 6.2.3 Prime expansions; 6.2.4 The Low Basis Theorem; 6.3 Product forcing; 6.4 MacDowell-Specker vs the uncountable; 6.4.1 No end extension; 6.4.2 Extensions with mutual generics; 6.4.3 Getting many classes; 6.5 Perfect generics; 6.6 Exercises; 6.7 Remarks & References; 7 Cuts; 7.1 Semiregular cuts |
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7.1.1 Semiregularity and WKL[sub(0)]7.2 Regular cuts; 7.3 Many faces of strongness; 7.4 Why PA?; 7.4.1 Schemes axiomatizing arithmetic; 7.5 Exercises; 7.6 Remarks & References; 8 Automorphisms of Recursively Saturated Models; 8.1 Moving undefinable elements; 8.2 Moving cuts and classes; 8.3 Moving gaps; 8.4 Back-and-forth; 8.5 Extending automorphisms; 8.6 Maximal automorphisms; 8.7 Fixing strong cuts; 8.8 Topology on the automorphism group; 8.9 Maximal point stabilizers; 8.10 Arithmetic saturation and open subgroups; 8.11 Exercises; 8.12 Remarks & References |
| Summary |
Aimed at graduate students, research logicians and mathematicians, this text covers over 40 years of work on relative classification theory for non-standard models of arithmetic |
| Bibliography |
Includes bibliographical references and indexes |
| Notes |
Print version record |
| Subject |
Peano, Giuseppe, 1858-1932.
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| SUBJECT |
Peano, Giuseppe, 1858-1932 fast |
| Subject |
Isomorphisms (Mathematics)
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Isomorphisms (Mathematics) -- Problems, exercises, etc
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Logic, Symbolic and mathematical -- Problems, exercises, etc
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Logic, Symbolic and mathematical.
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MATHEMATICS -- Infinity.
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MATHEMATICS -- Logic.
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Isomorphisms (Mathematics)
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Logic, Symbolic and mathematical
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Mathematische Logik
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Peano-Arithmetik
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Structurele vergelijkingen.
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Logica.
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| Genre/Form |
Electronic books
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exercise books.
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Problems and exercises
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Problems and exercises.
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Problèmes et exercices.
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| Form |
Electronic book
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| Author |
Schmerl, J. H. (James Henry), 1940- author.
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| ISBN |
9781435619227 |
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1435619226 |
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9780191524509 |
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0191524506 |
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9780191718199 |
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019171819X |
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