An overview of Saharon Shelah’s contributions to mathematical logic, in particular to model theory

Por • 12 sep, 2021 • Sección: Filosofía

∗Jouko Vaananen

I will give a brief overview of Saharon Shelah’s work in mathematical logic, especially in model theory. It is a formidable task given the sheer volume and broad spectrum of his work, but I will do my best, focusing on just a few main themes. In the statement that Shelah presented for the Schock Prize Committee he wrote: I would like to thank my students, collaborators, contemporary logicians, my teachers Haim Gaifman and Azriel Levy and my advisor Michael Rabin. I have been particularly influenced by Alfred Tarski, Michael Morley and Jerome Keisler. As it happens, in 1971 there was a birthday meeting in Berkeley in honor of Alfred Tarski. All of these people were there and gave talks. Shelah’s contribution to the Proceedings Volume of this meeting [5] is number 31 in the numbering of his papers, which now extends already to 1150. The papers are on the internet, often referred to by their “Shelah-number”. We sometimes tease Saharon by asking him what is in paper, say 716, and usually he knows it. Somebody once asked about a result and Saharon said it is in paper number 3. Three hundred what, asked the person, being used to the fact that Shelah has hundreds of papers, and Saharon answered, no, paper number 3. In fact paper number three [10] is a very influential paper for the development of model theory. Shelah made essentially three transformative contributions to the field of mathematical logic: stability theory, proper forcing and PCF theory, the first in model theory and the other two in set theory. He started as a model theorist and I think he still considers himself mainly as a model theorist, but he has extended his interest and work to set theory. Sigue en…

Department of Mathematics and Statistics University of Helsinki Finland March 7, 2020

https://helda.helsinki.fi//bitstream/handle/10138/315013/OnShelahsWork.pdf?sequence=2

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