Logic Seminar
David Marker
UIC
Computability of the countable saturated differentially closed field.
Abstract: It's been known since work of Harrington in the early 1970s that
computable differential fields have computable differential closures.
Recently Calvert, Frolov, Harizanov, Knight, McCoy, Soskova, and
Vatev showed that the countable saturated differentially closed field is computable.
Their proof involves first creating an effective listing of all types and then
using a result of Morley's on existence of computable saturated models.
I will give a significant simplification of the enumeration result and, for completeness,
sketch Morley's priority construction of a saturated model. Pillay has also
given an alternative enumeration argument though ours seems more robust
and generalizes to quantifier free types in ACFA.
Tuesday January 28, 2020 at 3:00 PM in 427 SEO