Lectures on Infinitary Model Theory (Lecture Notes in Logic) by David Marker

By David Marker

Infinitary good judgment, the good judgment of languages with infinitely lengthy conjunctions, performs a major position in version concept, recursion idea and descriptive set thought. This publication is the 1st sleek advent to the topic in 40 years, and should deliver scholars and researchers in all parts of mathematical good judgment as much as the edge of contemporary learn. The classical issues of back-and-forth structures, version lifestyles thoughts, indiscernibles and finish extensions are lined sooner than extra glossy themes are surveyed. Zilber's categoricity theorem for quasiminimal first-class sessions is proved and an software is given to covers of multiplicative teams. Infinitary equipment also are used to review uncountable types of counterexamples to Vaught's conjecture, and potent features of infinitary version idea are reviewed, together with an advent to Montalbán's fresh paintings on spectra of Vaught counterexamples. Self-contained introductions to powerful descriptive set concept and hyperarithmetic concept are supplied, as is an appendix on admissible version theory.

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