A Mysterious Ring
Alexandra Shlapentokh (East Carolina University)
Abstract: Let be the largest abelian extension of , or in other words the compositum of all cyclotomic extensions. Let be the ring of integers of or the ring of elements of satisfying monic irreducible polynomials over . It is not known whether the first-order theory of is decidable. is also a degree two extension of a totally real field. Much more is known about the first-order theory of rings of integers of totally real fields and in some cases one is able to deduce undecidability of the first-order theory of the ring of integers of a degree 2 extension of a totally real field from an analogous result for the ring of integers of the totally real field. However this method does not seem to work for . We discuss a possible way of resolving this problem and some related questions.
logicnumber theory
Audience: researchers in the topic
Series comments: Description: Seminar on all areas of logic
Organizer: | Wesley Calvert* |
*contact for this listing |