Computably Categorical Fields via Fermat’s Last Theorem

Article type: Research Article

Authors: Miller, Russell | Schoutens, Hans

Affiliations: Department of Mathematics, Queens College – C.U.N.Y. 65-30 Kissena Blvd. Flushing, New York 11367 U.S.A. Ph.D. Programs in Mathematics & Computer Science, C.U.N.Y. Graduate Center, 365 Fifth Avenue, New York, New York 10016 U.S.A. [email protected] qcpages.qc.cuny.edu/~rmiller | Department of Mathematics, New York City College of Technology, 300 Jay Street Brooklyn, New York 11201 U.S.A. Ph.D. Program in Mathematics, C.U.N.Y. Graduate Center, 365 Fifth Avenue, New York, New York 10016 U.S.A. [email protected], websupport1.citytech.cuny.edu/faculty/hschoutens/

Abstract: We construct a computable, computably categorical field of infinite transcendence degree over the rational numbers, using the Fermat polynomials and assorted results from algebraic geometry. We also show that this field has an intrinsically computable (infinite) transcendence basis.

Keywords: computability, computable categoricity, Fermat’s Last Theorem, fields, transcendence

DOI: 10.3233/COM-13017

Journal: Computability, vol. 2, no. 1, pp. 51-65, 2013