Zero-one laws for finitely presented structures

Abstract: Gromov proposed the notion of random groups as a model to study the typical behavior of finitely presented groups. They share many properties of the free group, and Knight conjectured that random groups satisfy the zero-one law and have the same first-order theory as the free group. In this joint work with Franklin and Knight, we study this zero-one law in other classes of structures. In particular, we consider random presentations in algebraic varieties in the sense of universal algebra. We will discuss some examples where the zero-one law holds and some other examples where the zero-one law fails. We also establish some general conditions for the zero-one law to hold (or fail).

logic

Audience: researchers in the topic

Computability theory and applications

Series comments: Description: Computability theory, logic

The goal of this endeavor is to run a seminar on the platform Zoom on a weekly basis, perhaps with alternating time slots each of which covers at least three out of four of Europe, North America, Asia, and New Zealand/Australia. While the meetings are always scheduled for Tuesdays, the timezone varies, so please refer to the calendar on the website for details about individual seminars.