Philip Welch
(University of Bristol)
Transfinite Dynamical Models

Various models generalising Turing's machine have been investigated with constraints of finite time (and possibly also space) being lifted. The most well known of these is the Infinite Time Turing machine of Hamkins and Kidder, but it is clear that many machines can be reconfigured to go transfinite, such as register machines (Koepke et al), or more recently Blum-Shub-Smale Machines (see Koepke-Seyfferth at this conference) all with differing characteristics.

Indeed there would seem to be many possibilities of transcending the machine inspiration and for the direct generalisation of dynamical systems (broadly conceived) into the transfinite. Probably this would result in varying degrees of significance. In general one would expect the transfinite to be very different from the finite version but nevertheless some leading to interesting mathematics.