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

By David Marker

Infinitary good judgment, the common sense of languages with infinitely lengthy conjunctions, performs a huge function in version concept, recursion conception and descriptive set thought. This ebook is the 1st smooth advent to the topic in 40 years, and should carry scholars and researchers in all parts of mathematical common sense as much as the edge of recent examine. The classical subject matters of back-and-forth structures, version life suggestions, indiscernibles and finish extensions are coated prior to extra sleek themes are surveyed. Zilber's categoricity theorem for quasiminimal very good periods is proved and an software is given to covers of multiplicative teams. Infinitary equipment also are used to check uncountable versions of counterexamples to Vaught's conjecture, and powerful points of infinitary version conception are reviewed, together with an creation to Montalbán's fresh paintings on spectra of Vaught counterexamples. Self-contained introductions to potent descriptive set conception and hyperarithmetic conception are supplied, as is an appendix on admissible version theory.

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