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Marker, D.:Lectures on Infinitary Model Theory (Lecture Notes in Logic 46). VIII, 183 pp., Cambridge University Press, Cambridge, 2016. £80,00.
Marker’s “Lectures on Infinitary Model Theory” gives a broad introduction to the model theory of infinitary languages and is intended for advanced graduate students, who have some familiarity with standard results of model, as well as set theory. The material is very well organized and structured: The text not only presents the most central results in the field, but also provides plenty of examples, as well as exercises. As stated by the author, the book is intended to prepare the reader for more recent advances in the area, and in particular recent work on abstract elementary classes. Furthermore, it contains many valuable references to the literature. The second half of the book contains an introduction to the subject of effective descriptive set theory, emphasizing the interplay between descriptive set theory and model theory. A recurrent...