
Lectures on Infinitary Model Theory
David Marker(Author)
Cambridge University Press
Published on 27. October 2016
Book
Hardback
192 pages
978-1-107-18193-9 (ISBN)
Description
Infinitary logic, the logic of languages with infinitely long conjunctions, plays an important role in model theory, recursion theory and descriptive set theory. This book is the first modern introduction to the subject in forty years, and will bring students and researchers in all areas of mathematical logic up to the threshold of modern research. The classical topics of back-and-forth systems, model existence techniques, indiscernibles and end extensions are covered before more modern topics are surveyed. Zilber's categoricity theorem for quasiminimal excellent classes is proved and an application is given to covers of multiplicative groups. Infinitary methods are also used to study uncountable models of counterexamples to Vaught's conjecture, and effective aspects of infinitary model theory are reviewed, including an introduction to Montalban's recent work on spectra of Vaught counterexamples. Self-contained introductions to effective descriptive set theory and hyperarithmetic theory are provided, as is an appendix on admissible model theory.
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 15 mm
Weight
437 gr
ISBN-13
978-1-107-18193-9 (9781107181939)
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Schweitzer Classification
Other editions
Additional editions

David Marker
Lectures on Infinitary Model Theory
E-Book
10/2016
Cambridge University Press
€93.49
Available for download

David Marker
Lectures on Infinitary Model Theory
E-Book
08/2016
Cambridge University Press
€103.99
Available for download
Person
David Marker is LAS Distinguished Professor of Mathematics at the University of Illinois, Chicago, and a Fellow of the American Mathematical Society. His main area of research is model theory and its connections to algebra, geometry and descriptive set theory. His book, Model Theory: An Introduction, is one of the most frequently used graduate texts in the subject and was awarded the Shoenfield Prize for expository writing by the Association for Symbolic Logic.
Content
Introduction; Part I. Classical Results in Infinitary Model Theory: 1. Infinitary languages; 2. Back and forth; 3. The space of countable models; 4. The model existence theorem; 5. Hanf numbers and indiscernibles; Part II. Building Uncountable Models: 6. Elementary chains; 7. Vaught counterexamples; 8. Quasinimal excellence; Part III. Effective Considerations: 9. Effective descriptive set theory; 10. Hyperarithmetic sets; 11. Effective aspects of L?1,?; 12. Spectra of Vaught counterexamples; Appendix A. N1-free abelian groups; Appendix B. Admissibility; References; Index.