关于算术函数域的初等等价、同构与同构

可定义（最大）余有限群的同构类型

Isomorphism types of definable (maximal) cofinitary groups

本文研究了可定义最大余有限群的同构类型，证明了特定余有限表示的存在性，并构造了相关算术最大余有限群。

基本等价与同构

Elementary equivalence versus Isomorphism

如何一阶语言的领域编码双有理不变量的品种？.这个问题与代数/算术几何中簇和有效性上的有理点有关。

On Interpretations in Büchi Arithmetics

Büchi arithmetics BA_n, n >= 2, are extensions of Presburger arithmetic with an unary functional symbol V_n(x) denoting the largest power of n that divides x. Definability of a set in BA_n is equivalent to its recognizability by a finite automaton receiving numbers in their n-ary expansion. We show that Büchi arithmetics BA_n and BA_m are bi-interpretable for any n,m. Furthermore, we establish that any interpretation of some structure in BA_n is isomorphic to some one-dimensional interpretation; however, this isomorphism must not be BA_n-definable.

关于一类Peano算术模型的值群

On the Value Group of a Model of Peano Arithmetic

本文研究了$IPA$ -实封闭的域，即实封闭的域，它的非负锥是Peano算术的模型.我们证明了$IPA$ -实封闭的域的值群在剩余域中是指数群，且逆命题一般不成立。作为应用，我们分类（直到同构）可数递归饱和指数实封闭的域的值群。利用这一特征，我们构造了可数指数实闭域，它们不是$IPA$ -实封闭的域.

无幂次的分类性

Categoricity without Power

论文证明了在递归理论中用算术度代替基数的Morrey分类性定理的类比，证明了D分类性理论的等价性与不可数分类性。

Word problems and ceers

This note addresses the issue as to which ceers can be realized by word problems of computably enumerable (or, simply, c.e.) structures (such as c.e. semigroups, groups, and rings), where being realized means to fall in the same reducibility degree (under the notion of reducibility for equivalence relations usually called "computable reducibility"), or in the same isomorphism type (with the isomorphism induced by a computable function), or in the same strong isomorphism type (with the isomorphism induced by a computable permutation of the natural numbers). We observe for instance that every ce…