Preliminaries: Banach space models -- Semidefinability of types -- Maurey strong types and convolutions -- Fundamental sequences -- Quantifier-free types over Banach spaces -- Digression: Ramsey's theorem for analysis -- Spreading models -- ℓp- and c₀ -types -- Extensions of operators by ultrapowers -- Where does the number p come from? -- Block representability of ℓp in types -- Krivine's theorem -- Stable Banach spaces -- Block representabiltiy of ℓp in types over stable spaces -- ℓp-subspaces of stable Banach spaces.