Sinossi
This volume presents research by algebraists and model theorists in accessible form for advanced undergraduates or beginning graduate students studying algebra, logic, or model theory. It introduces a general method for building infinite mathematical structures and surveys applications in algebra and model theory. A multi-step procedure, the method resembles a two-player game that continues indefinitely. This approach simplifies, motivates, and unifies a wide range of constructions.
Starting with an overview of basic model theory, the text examines a variety of algebraic applications, with detailed analyses of existentially closed groups of class 2. It describes the classical model-theoretic form of this method of construction, which is known as "omitting types," "forcing," or the "Henkin-Orey theorem," The final chapters are more specialized, discussing how the idea can be used to build uncountable structures. Applications include completeness for Magidor-Malitz quantifiers, Shelah's recent and sophisticated omitting types theorem for L(Q), and applications to Boolean algebras and models of arithmetic. More than 160 exercises range from elementary drills to research-related items, with further information and examples.
Starting with an overview of basic model theory, the text examines a variety of algebraic applications, with detailed analyses of existentially closed groups of class 2. It describes the classical model-theoretic form of this method of construction, which is known as "omitting types," "forcing," or the "Henkin-Orey theorem," The final chapters are more specialized, discussing how the idea can be used to build uncountable structures. Applications include completeness for Magidor-Malitz quantifiers, Shelah's recent and sophisticated omitting types theorem for L(Q), and applications to Boolean algebras and models of arithmetic. More than 160 exercises range from elementary drills to research-related items, with further information and examples.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
Contenuti
1. Preliminaries 2. Games and Forcing 3. Existential Closure 4. Chaos or Regimentation 5. Classical Languages 6. Proper Extensions 7. Generalised Quantifiers 8. L(Q) in Higher Cardinalities List of types of forcing List of open questions Bibiliography Index
Product Description
Book by Wilfrid Hodges
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Building Models by Games (Dover Books on Mathematics)
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Building Models by Games (Dover Books on Mathematics)
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paperback. Condizione: Good. Softcover bound in glossy pictorial paper. Mild edge wear to covers and crown and foot of spine. Binding is tight and secure. Pages are crisp, clean, and bright. Dover Publications. No date on title page. Copyright dated 1985. Stated 2006 edition. 318 pages. A good copy. We ship everyday from a real neighborhood bookstore. This description is written by an actual person, who is holding the book in front of them to make sure it?s properly described. Please contact us with questions or if you would like to see photographs. Codice articolo F-13066
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