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Building Models by Games (London Mathematical Society Student Texts, Series Number 2) - Softcover

 
9780521317160: Building Models by Games (London Mathematical Society Student Texts, Series Number 2)

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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.

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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.

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9780486450179: Building Models by Games (Dover Books on MaTHEMA 1.4tics)

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ISBN 10:  0486450171 ISBN 13:  9780486450179
Verlag: Dover Publications Inc, 2006
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Hodges, Wilfrid
ISBN 10: 0521317169 ISBN 13: 9780521317160
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Zustand: Good. Cambridge University Press, 1985. Cover lightly rubbed/bumped, unevenly sunned, corners faintly rubbed/bumped, spine sunned, spine ends faintly rubbed/bumped; edges very lightly soiled/bumped; erasures on Title page; binding tight; cover, edges, and interior intact and clean except as noted. paperback. Good. Bestandsnummer des Verkäufers 623006

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Hodges, Wilfrid
ISBN 10: 0521317169 ISBN 13: 9780521317160
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Hodges, W.
ISBN 10: 0521317169 ISBN 13: 9780521317160
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Paper Bound. Zustand: Near Fine. First Edition. Bestandsnummer des Verkäufers 00030626

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