# A role for well-foundedness in symbolic dynamics

## Adrian R. D. Mathias

(ERMIT, Universite de la Reunion)

Lluis Alseda, of the Universitat Autonoma de Catalunya, and his co-workers formulated in 1993 some problems in topological dynamics concerning continuous functions and omega-limit sets, and involving iterations and ordinals. As a set theorist visiting Barcelona, my interest was aroused.

In this talk, I shall show how the Alseda problems in dynamics translate to questions about the well-foundedness of certain simply-definable trees, thus allowing classical results from descriptive set theory to be applied.

An unexpected aspect was that although the iterations concerned resembled the Cantor-Bendixson iterations which always stop at a countable stage, the Alseda iterations proved in some instances to continue till the first uncountable ordinal.

The links to the PDF abstract and handout of the talk are listed below:

https://www.dropbox.com/s/w9pbpdgi12lflz5/swanabst.pdf?dl=0

https://www.dropbox.com/s/c68t0jnuhzkjv50/swanshortabst.pdf?dl=0

**Tuesday 19th July 2016, 14:00**

Faraday Lecture Theatre J

Department of Computer Science