# 23/09 — Alfredo Roque Freire

Foundations of infinitary and finitary proofs in the context of metatheories
Alfredo Roque Freire, mestrando IFCH/CLE – Unicamp
This presentation aims to put into perspective the infinitary and finitary proofs of meta-theoretical results. On the one hand, we seek to clarify which means a result grounded in model theoretical techniques and, on the other hand, we develop the argument that there is a real gain in the exposure of a finitary proof. More specically, we have based our discussion on the two proofs of relative consistency between ZFC and NBG: first, the widely used model theoretical proof, second, the finitary proof given by Schoeneld in 1954.
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