Lectures on Infinitary Model Theory (Lecture Notes in Logic #46) (Hardcover)

Lectures on Infinitary Model Theory (Lecture Notes in Logic #46) By David Marker Cover Image
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This is book number 46 in the Lecture Notes in Logic series.


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 Montalb n'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.

Product Details
ISBN: 9781107181939
ISBN-10: 1107181933
Publisher: Cambridge University Press
Publication Date: October 27th, 2016
Pages: 192
Language: English
Series: Lecture Notes in Logic