Decidability and Computability of Certain Torsion-Free Abelian Groups

نویسندگان

Rodney G. Downey

Sergei S. Goncharov

Asher M. Kach

Julia F. Knight

Oleg V. Kudinov

Alexander G. Melnikov

Daniel Turetsky

چکیده

We study completely decomposable torsion-free abelian groups of the form GS := ⊕n∈SQpn for sets S ⊆ ω. We show that GS has a decidable copy if and only if S is Σ2 and has a computable copy if and only if S is Σ 0 3.

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

Kulikov’s problem on universal torsion-free abelian groups revisited

Let T be a torsion abelian group. We consider the class of all torsion-free abelian groups G satisfying Ext(G,T ) = 0 and search for λ-universal objects in this class. We show that for certain T there is no ω-universal group. However, for uncountable cardinals λ there is always a λ-universal group if we assume (V = L). Together with results by the second author this solves completely a problem ...

متن کامل

Advice Automatic Structures and Uniformly Automatic Classes

We study structures that are automatic with advice. These are structures that admit a presentation by finite automata (over finite or infinite words or trees) with access to an additional input, called an advice. Over finite words, a standard example of a structure that is automatic with advice, but not automatic in the classical sense, is the additive group of rational numbers (Q,+). By using ...

متن کامل

On categories of merotopic, nearness, and filter algebras

We study algebraic properties of categories of Merotopic, Nearness, and Filter Algebras. We show that the category of filter torsion free abelian groups is an epireflective subcategory of the category of filter abelian groups. The forgetful functor from the category of filter rings to filter monoids is essentially algebraic and the forgetful functor from the category of filter groups to the cat...

متن کامل

Cotorsion theories cogenerated by א1-free abelian groups

Given an א1-free abelian group G we characterize the class CG of all torsion abelian groups T satisfying Ext(G, T ) = 0 assuming the special continuum hypothesis CH. Moreover, in Gödel’s constructable universe we prove that this characterizes CG for arbitrary torsion-free abelian G. It follows that there exist some ugly א1-free abelian groups.

متن کامل