Aimed at graduate students, this book addresses the need for a comprehensive introductory text in mathematical logic. It not only covers essential concepts but also encourages readers to delve deeper into the subject. By filling the existing gap in available literature, the author seeks to inspire further exploration and study in mathematical logic.
Delving into the interplay between infinitary model theory and various branches of mathematical logic, this work highlights significant algebraic applications. It presents a comprehensive examination of how these connections can enhance understanding and offer new insights within the field.
Focusing on model theory's applications to algebra, this modern introduction covers classical topics like model construction, type spaces, and prime models, while also delving into stability theory, including Morley's Categoricity Theorem. Unique to this text are chapters on omega-stable groups and the geometry of strongly minimal sets, which are often overlooked in other introductions. The author further illustrates the relevance of these concepts through Hrushovski's contributions to diophantine geometry, providing a comprehensive and innovative perspective on the subject.
Assumes only a familiarity with algebra at the beginning graduate level; Stresses applications to algebra; Illustrates several of the ways Model Theory can be a useful tool in analyzing classical mathematical structures