Analysis and Logic [Paperback]

This volume comprises articles from four outstanding researchers who work at the cusp of analysis and logic.This volume comprises articles from four outstanding researchers who work at the cusp of analysis and logic. The emphasis is on active research topics; many results are presented that have not been published before and open problems are formulated. Considerable effort has been made by the authors to integrate their articles and make them accessible to mathematicians new to the area.This volume comprises articles from four outstanding researchers who work at the cusp of analysis and logic. The emphasis is on active research topics; many results are presented that have not been published before and open problems are formulated. Considerable effort has been made by the authors to integrate their articles and make them accessible to mathematicians new to the area.This volume presents articles from four outstanding researchers who work at the cusp of analysis and logic. The emphasis is on active research topics; many results are presented that have not been published before and open problems are formulated. Considerable effort has been made by the authors to make their articles accessible to mathematicians new to the areaIntroduction; Part I. Ultraproducts in Analysis: 1. Introduction; 2. Normed space structures; 3. Signatures; 4. Ultrapowers of normed space structures; 5. Positive bounded formulas; 6. Basic model theory; 7. Quantifier-free formulas; 8. Ultraproducts of normed space structures; 9. Basic model theory II; 10. Isomorphic ultrapowers; 11. Alternative formulations of the theory; 12. Homogeneous structures; 13. More model theory; 14. Types; References; Index; Part II. Actions of Polish Groups and Classification Problems: 1. Introduction; 2. The general Glimm-Effros dichotomy; 3. Actions of polish groups; 4. Actions of countable groups; 5. Actions of locally compact groups; 6. Actions of the infinite symmetric group; 7. Turbulence I: overview; 8. Turbulenl³#