Description

Book Synopsis
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.

Table of Contents
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 Lω1,ω; 12. Spectra of Vaught counterexamples; Appendix A. N1-free abelian groups; Appendix B. Admissibility; References; Index.

Lectures on Infinitary Model Theory

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    A Hardback by David Marker

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      Publisher: Cambridge University Press
      Publication Date: Publication Date: 10/27/2016 12:00:00 AM
      ISBN13: 9781107181939, 978-1107181939
      ISBN10: 1107181933
      Also in:
      Algebraic geometry Mathematical logic Set theory

      Description

      Book Synopsis
      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.

      Table of Contents
      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 Lω1,ω; 12. Spectra of Vaught counterexamples; Appendix A. N1-free abelian groups; Appendix B. Admissibility; References; Index.

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