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Informationen zum Autor David Marker is LAS Distinguished Professor of Mathematics at the University of Illinois, Chicago, and a Fellow of the American Mathematical Society. His main area of research is model theory and its connections to algebra, geometry and descriptive set theory. His book, Model Theory: An Introduction, is one of the most frequently used graduate texts in the subject and was awarded the Shoenfield Prize for expository writing by the Association for Symbolic Logic. Klappentext Explores connections between infinitary model theory and other branches of mathematical logic, with algebraic applications. Zusammenfassung This book is the first modern introduction to the logic of infinitary languages in forty years! and is aimed at graduate students and researchers in all areas of mathematical logic. Connections between infinitary model theory and other branches of mathematical logic! and applications to algebra and algebraic geometry are both comprehensively explored. Inhaltsverzeichnis Introduction; Part I. Classical Results in Infinitary Model Theory: 1. Infinitary languages; 2. Back and forth; 3. The space of countable models; 4. The model existence theorem; 5. Hanf numbers and indiscernibles; Part II. Building Uncountable Models: 6. Elementary chains; 7. Vaught counterexamples; 8. Quasinimal excellence; Part III. Effective Considerations: 9. Effective descriptive set theory; 10. Hyperarithmetic sets; 11. Effective aspects of L¿1,¿; 12. Spectra of Vaught counterexamples; Appendix A. N1-free abelian groups; Appendix B. Admissibility; References; Index.
