Logic Seminar
John Baldwin
UIC
Why the weak GCH is true!
Abstract: By the weak GCH we mean the assertion: 2^\lambda < 2^{\lambda^+}. We will
argue for the acceptance of this axiom on grounds of its coherence with our
intuitions of cardinal arithmetic and its consequences for mathematical
practice. The second argument is mediated by the Devlin-Shelah weak diamond. We
will explain this principle, which follows easily from weak GCH, and discuss
some of its consequences. These include a version of Morley\'s theorem for
L_{\omega_1,\omega} (Shelah) and implications for the study of semi-abelian
varieties (Zilber).
The goal of the talk will be to derive Weak Diamond from weak GCH, sketch a bit of context/consequences, and pose some open problems.
Tuesday January 23, 2007 at 3:00 PM in SEO 427