Abstract: One of the most important results concerning PA (= Peano Arithmetic) is the main theorem of the paper of R. MacDowell and E. Specker Modelle der Arithmetik. (German) 1961 Infinitistic Methods (Proc. Sympos. Foundations of Math., Warsaw, 1959) pp. 257–263 Pergamon, Oxford; Państwowe Wydawnictwo Naukowe, Warsaw.

My aim is to briefly present work motivated by this result; in particular, I will discuss attempts at miniaturizing this theorem, i.e., proving variants of it for fragments of PA, like I\Sigma_n (\Sigma_n-induction), B\Sigma_n (\Sigma_n-collection) etc.

L’exposé est disponible ici