Turing Degrees of Isomorphism Types of Geometric Objects

Article type: Research Article

Authors: Calvert, Wesley | Harizanov, Valentina | Shlapentokh, Alexandra

Affiliations: Department of Mathematics, Southern Illinois University, Mail Code 4408, 1245 Lincoln Drive, Carbondale, Illinois 62901, USA. [email protected] | Department of Mathematics, George Washington University, Washington, DC 20052, USA. [email protected] | Department of Mathematics, East Carolina University, Greenville, NC 27858, USA. [email protected]

Abstract: We initiate the computability-theoretic study of ringed spaces and schemes. In particular, we show that any Turing degree may occur as the least degree of an isomorphic copy of a structure of these kinds. We also show that these structures may fail to have a least degree.

Keywords: Turing degrees, isomorphism types, varieties, ringed spaces, schemes

DOI: 10.3233/COM-140029

Journal: Computability, vol. 3, no. 2, pp. 105-134, 2014