Logic Seminar
John Baldwin
UIC
Henkin models in the continuum
Abstract: We describe Shelah’s construction of atomic models in the continuum, as reformulated with Laskowski as a Henkin construction [2]. Then we discuss briefly the connection with the Ackerman-Freer-Patel [1] proof that if $M$ is a countable structure for
a relational language $L$ with trivial definable closure then there is an invariant probability measures on the countable $L$-structures that concentrates on $M$. We explain
while the sufficient conditions for the model in the continuum include those with trivial definable closure, our theorem applies more generally to obtaining a atomic model
in the continuum of the first order theory of a countable atomic extendible structure
admitting a formula-based geometry.
[1] Ackerman, N. and Freer, C. and Patel, R., Invariant measures concentrated
on countable structures, Forum of Mathematics, Sigmas, vol. 4 (2016), no. X, pp. 59.
[2] Baldwin, J. T. and Laskowski, M.C., Henkin Constructions of Models in the
Continuum, Bulletin of Symbolic Logic, vol. 24(2019), no. 1, pp. 1–34.
Tuesday March 10, 2020 at 3:00 PM in 427 SEO