Building Models by Games

Wilfrid Hodges (Autor)

Buch | Softcover

320 Seiten

1985
Cambridge University Press (Verlag)
978-0-521-31716-0 (ISBN)

Infos

This book introduces a general method for building infinite mathematical structures, and surveys its applications in algebra and model theory. The basic idea behind the method is to build a structure by a procedure with infinitely many steps, similar to a game between two players that goes on indefinitely. The approach is new and helps to simplify, motivate and unify a wide range of constructions that were previously carried out separately and by ad hoc methods. The first chapter provides a resume of basic model theory. A wide variety of algebraic applications are studied, with detailed analyses of existentially closed groups of class 2. Another chapter describes the classical model-theoretic form of this method -of construction, which is known variously as 'omitting types', 'forcing' or the 'Henkin-Orey theorem'. The last three chapters are more specialised and discuss how the same idea can be used to build uncountable structures. Applications include completeness for Magidor-Malitz quantifiers, and Shelah's recent and sophisticated omitting types theorem for L(Q). There are also applications to Bdolean algebras and models of arithmetic.

Produkt-Details

• Erscheint lt. Verlag: 2.5.1985
• Reihe/Serie: London Mathematical Society Student Texts
• Zusatzinfo: Worked examples or Exercises
• Verlagsort: Cambridge
• Sprache: englisch
• Maße: 152 x 228 mm
• Gewicht: 468 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
• Themenwelt: Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
• Schlagworte: London Mathematical Society Student Texts S.; 2
• ISBN-10: 0-521-31716-9 / 0521317169
• ISBN-13: 978-0-521-31716-0 / 9780521317160
• Zustand: Neuware