Oliver Thewalt

    Oliver Thewalt

    Theoretical Physics | Quantum Biology | Dark Matter Research Cluster

    General topology meets model theory, on p and t, via Professor Jonathan Vos Post

    http://www.pnas.org/content/110/33/13300.full

    01:30:15

    Thanks Jonathan  

    I can't help it, I was about to log off, but I love this post, I could do this for my entire life, can't someone grant me a scholarship, fellows??!


    Abstract

    Cantor proved in 1874 [Cantor G (1874) J Reine Angew Math 77:258–262] that the continuum is uncountable, and Hilbert’s first problem asks whether it is the smallest uncountable cardinal. A program arose to study cardinal invariants of the continuum, which measure the size of the continuum in various ways. By Gödel [Gödel K (1939) Proc Natl Acad Sci USA 25(4):220–224] and Cohen [Cohen P (1963) Proc Natl Acad Sci USA 50(6):1143–1148], Hilbert’s first problem is independent of ZFC (Zermelo-Fraenkel set theory with the axiom of choice). Much work both before and since has been done on inequalities between these cardinal invariants, but some basic questions have remained open despite Cohen’s introduction of forcing. The oldest and perhaps most famous of these is whether “Graphic,” which was proved in a special case by Rothberger [Rothberger F (1948) Fund Math 35:29–46], building on Hausdorff [Hausdorff (1936) Fund Math 26:241–255]. In this paper we explain how our work on the structure of Keisler’s order, a large-scale classification problem in model theory, led to the solution of this problem in ZFC as well as of an a priori unrelated open question in model theory.