Title: Formalizing Gödel's System T in Lean Speaker: Horațiu Cheval (University of Bucharest) Abstract: In 1958, Gödel introduced his functional interpretation as a method of reducing the consistency of first-order arithmetic to that of a quantifier-free system of primitive recursive functionals of higher type. His work has since enabled other advances in proof theory, notably …

Title: Unwinding of proofs Speaker: Pedro Pinto (TU Darmstadt) Abstract: The unwinding of proofs program dates back to Kreisel in the fifties and rests on the following broad question: “What more do we know if we have proved a theorem by restricted means than if we merely know that it is true?”   This research …

Title:  Exponential Diophantine equations over ℚ Speaker: Mihai Prunescu (University of Bucharest & IMAR) Abstract: In a previous exposition we have seen that the solvability over ℚ is undecidable for systems of exponential Diophantine equations. We now show that the solvability of individual exponential Diophantine equations is also undecidable, and that this happens as well …

Title: A proof mining case study on the unit interval Speaker: Andrei Sipoș (University of Bucharest & IMAR) Abstract:  In 1991, Borwein and Borwein proved the following: if L>0, f : → is L-Lipschitz, (xn), (tn) ⊆ are such that for all n, xn+1=(1-tn)xn+tnf(xn) and there is a δ>0 such that for all n, tn≤(2-δ)/(L+1), then …