# Infinite-Time Turing Machines and Borel Reducibility

@inproceedings{Coskey2009InfiniteTimeTM, title={Infinite-Time Turing Machines and Borel Reducibility}, author={Samuel Coskey}, booktitle={CiE}, year={2009} }

In this document I will outline a couple of recent developments, due to Joel Hamkins, Philip Welch and myself, in the theory of infinite-time Turing machines. These results were obtained with the idea of extending the scope of the study of Borel equivalence relations, an area of descriptive set theory. I will introduce the most basic aspects of Borel equivalence relations, and show how infinite-time computation may provide insight into this area.

## 3 Citations

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Considerations of what may lay on an output tape at an infinite stage first surface in the notion of ‘computation in the limit’ or ‘limit decidable’ are considered.

### Recognizable sets and Woodin cardinals: computation beyond the constructible universe

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### The Lost Melody Phenomenon

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It is proved that, for unresetting infinite time register machines introduced by P. Koepke, recognizability equals computability, i.e. the lost melody phenomenon does not occur.

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