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Seminar

Nondefinability of Rings of Integers in Algebraic Extensions of the Rationals August 03, 2022 (02:15 PM PDT - 03:00 PM PDT)
Parent Program:
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Speaker(s) Arno Fehm (TU Dresden)
Description No Description
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Nondefinability Of Rings Of Integers In Algebraic Extensions Of The Rationals

Abstract/Media

Complementing the various methods to define subrings of fields, I will state a few general principles that tell us a priori that subrings of certain fields cannot possibly be definable (or at least not existentially definable). I will then discuss joint work with Philip Dittmann in which we determine the common theory of (in a precise sense) ``almost all'' algebraic extensions of the field of rational numbers, in order to conclude that almost all such extensions have no definable proper subrings at all, strengthening a recent result by Eisentr\"ager, Miller, Springer and Westrick.

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Nondefinability Of Rings Of Integers In Algebraic Extensions Of The Rationals