科研之友
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摘要
For the ring of integers O of a totally real algebraic field, Julia Robinson defines a set A(O) such that either A(O) = {+infinity} or it is an interval in R. She then proves that if this set has a minimum, then the natural numbers can be defined in O, and hence O has undecidable first-order theory. All known examples are such that A(O) has a minimum which is either 4 or +infinity. In this work, we construct two infinite families of subrings of such rings for which inf(A(O)) is strictly between 4 and +infinity. In one family, the infimum is a minimum, whereas in the other family it is not, but we can still define the natural numbers in this case.
- 出版日期2015-10
