一致项与局部元素

Uniform bounds on growth in o-minimal structures

We prove that a function definable with parameters in an o-minimal structure is bounded away from infinity as its argument goes to infinity by a function definable without parameters, and that this new function can be chosen independently of the parameters in the original function. This generalizes a result in a paper of Friedman and Miller. Moreover, this remains true if the argument is taken to approach any element of the structure (or plus/minus infinity), and the function has limit any element of the structure (or plus/minus infinity).

Relation between the Usual Order and the Enumeration Orders of Elements of r.e. Sets

In this paper, we have compared r.e. sets based on their enumeration orders with Turing machines. Accordingly, we have defined novel concept uniformity for Turing machines and r.e. sets and have studied some relationships between uniformity and both one-reducibility and Turing reducibility. Furthermore, we have defined type-2 uniformity concept and studied r.e. sets and Turing machines based on this concept. In the end, we have introduced a new structure called Turing Output Binary Search Tree that helps us lighten some ideas.

Local reflection, definable elements and 1-provability

In this note we study several topics related to the schema of local reflection $\mathsf{Rfn}(T)$ and its partial and relativized variants. Firstly, we introduce the principle of uniform reflection with $Σ_n$-definable parameters, establish its relationship with the relativized local reflection principles and corresponding versions of induction with definable parameters. Using this schema we give a new model-theoretic proof of the $Σ_{n+2}$-conservativity of uniform $Σ_{n+1}$-reflection over relativized local $Σ_{n+1}$-reflection. We also study the proof-theoretic strength of Feferman's theorem…

直觉主义逻辑中的一致局部表格性

Uniform Local Tabularity in Intuitionistic Logic

本文研究直觉主义逻辑中一致局部表格性的强化概念，通过Heyting代数的迭代蕴涵生成，证明n一致局部有限Heyting代数构成簇，并给出n<3时的公理化，同时构造反例回答Shehtman问题。

一致局部弱 o-极小性与 $*$-局部弱 o-极小性

Uniform local weak o-minimality and $*$-local weak o-minimality

本文引入一致局部弱 o-极小性与 $*$-局部弱 o-极小性，并证明相关结构在一元 $*$-连续性性质下的局部单调性定理及可定义集维数公式。