Archive of events from 2017
An archive of events from the year

Research Lindström Lecture: Albert Visser (Emeritus Professor of Philosophy at Utrecht University)
The Second Incompleteness Theorem in a (somewhat) General Setting
We study the Second Incompleteness Theorem, G2, in the Fefermanstyle. This means that we work with a fixed provabilitypredicate but allow the representations of the axiom set to vary. Feferman observed that the axiom set of Peano Arithmetic, PA, has a Π01representation for which PA proves its own consistency.
We isolate a condition that Feferman’s example fails to satisfy. This condition gives a reasonably general version of G2. We show that this version yields a proof of G2 for Σ01seminumerations of the axiom set which works even if the theory itself is not recursively enumerable. We discuss an interesting example that illustrates that we may have G2 even in the absence of the Löb conditions.

Public Lindström Lecture: Albert Visser (Emeritus Professor of Philosophy at Utrecht University)
De Interpretatione
Per Lindström’s work on interpretations has great beauty. He was a grand master of dazzling diagonal arguments. In this talk we will explain the basic setting underlying Per’s work. We introduce the notion of interpretation and provide some examples of interpretations. We show how, in the context of arithmetic, the notion of interpretability has an almost unrecognizable equivalent. This equivalence is known as the Orey–Hájek Characterization.
We will discuss some results of Per and have a look at further developments.