Nov 19 2019

Logic Seminar: Connectedness in structures on the real numbers: o-minimality and undecidability, by Chris Miller

November 19, 2019

3:30 PM - 4:20 PM

Location

427 SEO

Address

Chicago, IL

Chris Miller (The Ohio State University ): Connectedness in structures on the real numbers: o-minimality and undecidability

We consider structures on the set of real numbers having the property that connected components of definable sets are definable. All o-minimal structures on the real line (R,<) have the property, as do all expansions of the real field that define the set N of natural numbers. Our main analytic-geometric result is that any such expansion of (R,<,+) by boolean combinations of open sets (of any arities) is either o-minimal or undecidable. We also show that expansions of (R, <, N) by subsets of N^n (n allowed to vary) have the property if and only if all arithmetic sets are definable. (Joint with A. Dolich, A. Savatovsky and A. Thamrongthanyalak.) Please click here to make changes to, or delete, this seminar announcement.

Contact

James Freitag

Date posted

Oct 22, 2019

Date updated

Oct 22, 2019

Speakers

Chris Miller | (The Ohio State University )