Computably Categorical Fields via Fermat's Last Theorem

نویسندگان

  • Russell Miller
  • Hans Schoutens
چکیده

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

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

D-computable Categoricity for Algebraic Fields

We use the Low Basis Theorem of Jockusch and Soare to show that all computable algebraic fields are d-computably categorical for a particular Turing degree d with d′ = 0′′, but that not all such fields are 0′-computably categorical. We also prove related results about algebraic fields with splitting algorithms, and fields of finite transcendence degree over Q.

متن کامل

Categoricity Properties for Computable Algebraic Fields

We examine categoricity issues for computable algebraic fields. Such fields behave nicely for computable dimension: we show that they cannot have finite computable dimension greater than 1. However, they behave less nicely with regard to relative computable categoricity: we give a structural criterion for relative computable categoricity of these fields, and use it to construct a field that is ...

متن کامل

INHERITANCE AND REGENERATION OF CYTOPLASMIC DAMAGE IN Paramecium Aurelia.

IH. S. Vandiver, "Fermat's Last Theorem," Am. Math. Mlonthly, 53, 567-568, 1946. 2 H. S. Vandiver, "The Relation of Some Data Obtained from Rapid Computing Machines to the Theory of Cyclotomic Fields, these PROCEEDINGS, 40, 474-480, 1954. 3H. S. Vandiver, "A Theorem of Kummer's concerning the Second Factor of the Class Number of a Cyclotomic Field," Bull. Am. Math. Soc., 35, 333-335, 1929. 4D. ...

متن کامل

A computably stable structure with no Scott family of finitary formulas

One of the goals of computability theory is to find syntactic equivalences for computational properties. The Limit Lemma is a classic example of this type of equivalence: X ⊆ ω is computable from 0′ if and only if it is arithmetically definable by a ∆2 formula. A more relevant example for this paper was proved independently by Ash, Knight, Manasse and Slaman [1] and by Chishom [2]: a computable...

متن کامل

Proof for the Beal conjecture and a new proof for Fermat's last theorem

The Beal Conjecture was formulated in 1997 and presented as a generalization of Fermat's Last Theorem, within the number theory ́s field. It states that, for X, Y, Z, n , n and n positive integers with n , n , n > 2, if X + Y = Z then X, Y, Z must have a common prime factor. This article presents the proof for the Beal Conjecture, obtained from the correspondences between the real solutions of t...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Computability

دوره 2  شماره 

صفحات  -

تاریخ انتشار 2013