VVISO DI SEMINARIO

Il Professore Fernando Ferreira dell'Università di Lisbona, giovedì 24 ottobre, alle ore 15:00, nell'aula G (ex Psicologia) del Dipartimento di Matematica e Fisica della Università degli Studi della Campania “Luigi Vanvitelli”,terrà il seguente seminario

A new take on proof mining

Abstract: Proof mining is a program whose aim is to formulate quantitative versions of theorems of mathematics and, from the proof of the theorem, extract explicit bounding information. In the first part of the talk, we emphasize the first aspect of proof mining. We give two examples, one in analysis, the other in algebra, where the so-called bounded functional interpretation helps in formulating appropriate quantitative versions. In the second part of the talk, we argue that some principles of the bounded functional interpretation - to wit the very same that guide the formulation of the quantitative versions - help in explaining why certain minings are possible. These principles generalize weak König’s lemma and yield conservation results, a particular case being Harvey Friedman’s well-known theorem. A curious feature is that these principles may be false (in contrast to weak König’s lemma) but, by conservativity, only have true quantitative consequences. We illustrate this latter feature with the discussion of a famous fixed point theorem of Felix Browder.