Speaker
Léon Probst
University of Italian Switzerland
Talks at this conference:
Wednesday, 15:15, J222 
Selfreferential Gödel numberings and uniformity 
In arithmetic, selfreference relies, among other things, on a correct choice of Gödel numbering. Interestingly, one can build selfreference directly into a numbering, which allows us to get the diagonal lemma for free, i.e. bypassing the usual arithmetic of the syntax. For this reason, selfreferential numberings are often considered inadequate in a philosophical interpretation of certain metamathematical theorem. However, it is difficult to impose a precise criterion on the numberings (such as monotonicity) to exclude these numberings. Most common criteria fail in this respect or seem unmotivated (cf. [1]). This talk introduces uniformity as a new criterion for numbering. First, we show that standard numberings (on the common conceptions of syntax), as well as other standard codings (e.g. of ordered pairs), are indeed uniform. Second, we show how our criterion excludes the nonstandard numberings, including the deviant and selfreferential ones. Finally, we discuss its philosophical motivations and some of its implications. Joint work with Balthasar Grabmayr. Bibliography
