University Seminar: Logic Across Disciplines- Building models of strongly minimal theories

Title: Building models of strongly minimal theories
Speaker: Steffen Lempp, University of Wisconsin-Madison-
Date and time: Friday, November 15, 11:00am-12 noon
Place: Phillips Hall (801 22nd Street), Room 736

Abstract: What information does one need to know in order to build the models of a strongly minimal theory? To answer this question, we first formalize it in two ways. Note that if a theory T has a computable model, then T ∩ ∃n is uniformly Σ0n. We call such theories Solovay theories. A degree is strongly minimal computing if it computes a copy of every model of every strongly minimal Solovay theory. A second notion, introduced by Lempp in the mid-1990's, is that of a strongly minimal relatively computing degree. A degree d is strongly minimal relatively computing if whenever T is a strongly minimal theory with one computable model, d computes a copy of every model of T. We characterize both classes of degrees as exactly the degrees which are high over 0'', i.e., d ≥ 0'' and d' ≥ 0(4).