Indiscernible sequences in Banach space geometry

0. Introduction 2 The impact of logic in Banach space theory 2 The case of model theory 2 Model theory for structures of functional analysis 3 Two famous applications 4 A note on the exposition 4 1. Preliminaries: Banach Space Models 5 Banach space structures and Banach space ultrapowers 5 Positive bounded formulas 7 Approximate satisfaction 8 (1 + )-isomorphism and (1 + )-equivalence of structures 10 Finite representability 12 Types 12 Saturated and homogeneous structures 13 The monster model 14 2. Semidefinability of Types 14 3. Maurey Strong Types and Convolutions 16 4. Fundamental sequences 18 5. Quantifier-Free Types over Banach Spaces 19 6. Digression: Ramsey’s Theorem for Analysis 21 7. Spreading models 22 8. `pand c0-Types 23 9. Extensions of Operators by Ultrapowers 25 10. Where Does the Number p Come From? 26 11. Block Representability of `p in Types 27 12. Krivine’s Theorem 28 13. Stable Banach Spaces 30 14. Block Representability of `p in Types Over Stable Spaces 31 15. `p-Subspaces of Stable Banach Spaces 32 16. Historical Remarks 35 References 39