The Cardinality of the second uniform indiscernible

通过强 ssp 力迫增加第二一致不可辨元

Increasing the second uniform indiscernible by strongly ssp forcing

本文提出一种新的平稳集保持力迫 $\mathbb P^{c-c}(λ,μ)$，在特定大基数假设下将第二一致不可辨元 $\mathbf{u}_2$ 增加至超越给定序数 $λ$，并利用双人捕获博弈控制力迫行为。

On uniform definability of types over finite sets

In this paper, using definability of types over indiscernible sequences as a template, we study a property of formulas and theories called "uniform definability of types over finite sets" (UDTFS). We explore UDTFS and show how it relates to well-known properties in model theory. We recall that stable theories and weakly o-minimal theories have UDTFS and UDTFS implies dependence. We then show that all dp-minimal theories have UDTFS.

On the Uniform Computational Content of Ramsey's Theorem

We study the uniform computational content of Ramsey's theorem in the Weihrauch lattice. Our central results provide information on how Ramsey's theorem behaves under product, parallelization and jumps. From these results we can derive a number of important properties of Ramsey's theorem. For one, the parallelization of Ramsey's theorem for cardinality $n\geq1$ and an arbitrary finite number of colors $k\geq2$ is equivalent to the $n$--th jump of weak Kőnig's lemma. In particular, Ramsey's theorem for cardinality $n\geq1$ is $Σ^0_{n+2}$--measurable in the effective Borel hierarchy, but not $Σ^…

Uniformization and the diversity of Whitehead groups

The connections between Whitehead groups and uniformization properties were investigated by the third author in [Sh:98]. In particular it was essentially shown there that there is a non-free Whitehead (respectively, aleph_1-coseparable) group of cardinality aleph_1 if and only if there is a ladder system on a stationary subset of omega_1 which satisfies 2-uniformization (respectively, omega-uniformization). These techniques allowed also the proof of various independence and consistency results about Whitehead groups, for example that it is consistent that there is a non-free Whitehead group of…

关于单调函数一致连续性的一点注记

A note on uniform continuity of monotone functions

本文证明在ZFC一致地，每个非递减函数在某个大小为连续统基数的子集上一致连续，并给出基数特征$\mathfrak d^*$的刻画及其与$\mathfrak u,\mathfrak r,\mathfrak d$的关系。