Section: New Results

Computability on quasi-Polish spaces

• Participants: Mathieu Hoyrup, Cristobal Rojas, Victor Selivanov, Donald Stull

Descriptive Set Theory (DST) is a branch of topology which interacts very nicely with computability and logic. Indeed, these three theories involve measuring the complexity of describing objects in different ways (respectively as combinations of open sets, by programs, by formulae), which are intimately related. However, DST is traditionally developed on spaces relevant to mathematical analysis (Polish spaces), but not to theoretical computer science. The recently introduced quasi-Polish spaces are a much broader class of spaces including for instance Scott domains, important in functional programming. However, how to compute in such spaces is still not well-understood. In particular, quasi-Polish spaces can be characterized in many ways, so one has to choose the right definition to start with. We compare the computable versions of some of them, proving their non-equivalence, and focus on one of them, providing evidence that this notion is probably the right one. This work was presented at DCFS 2019 [26].