In this talk we present the basics of Gödel logics and some of their properties, which leads us to the question of the total number of different Gödel logics (as sets of formulas). From there we will take a long detour via order theory, well-quasi- and better-quasi-orderings to a generalization of the famous Fraïssé conjecture from 1948.

This conjecture is concerned with the number of scattered linear orderings and their bi-embeddability, and was proven in the 70ies by Laver building on the work of Nash-Williams on various quasi-orderings in the 60ies. We extend this notion to continuous bi-embeddability, and show similar results to the original Fraïssé conjecture.

Finally, returning to Gödel logics, we make use of this result to obtain a suprising theorem on the number of Gödel logics.

Robert Recorde Room

Department of Computer Science