It is known that the pfaffian closure of an analytic o-minimal structure is model complete in the language of all nested Rolle leaves. However, the latter is not a functional language; the language of nested pfaffian functions is a functional language in which the pfaffian closure might be model complete as well.
Impact
The functional language of nested pfaffian maps allows for certain complexity and effectivity control that the language of nested Rolle leaves lacks. Knowing model completeness in the former language would be a big step towards understanding the full pfaffian closure of an o-minimal structure, with applications to diophantine geometry and neural networks.
Student Experience
Gareth was a postdoctoral fellow at McMaster.
Countries
Canada, United Kingdom
Impact
Research
Institutional Partner(s)
Community Partner(s)
Industry Partner(s)
Key Outcomes
Publications
Sponsorship
Federal Provincial Foreign
Sponsorship Details
NSERC discovery grant 261961, McMaster University, University of Manchester
