Generating ultrafilters in a reasonable way

Reasonable ultrafilters, again

We continue investigations of reasonable ultrafilters on uncountable cardinals defined in math.LO/0407498. We introduce stronger properties of ultrafilters and we show that those properties may be handled in lambda-support iterations of reasonably bounding forcing notions. We use this to show that consistently there are reasonable ultrafilters on an inaccessible cardinal lambda with generating system of size less than 2^lambda . We also show how reasonable ultrafilters can be killed by forcing notions which have enough reasonable completeness to be iterated with lambda-supports (and we show th…

The combinatorics of reasonable ultrafilters

We are interested in generalizing part of the theory of ultrafilters on omega to larger cardinals. Here we set the scene for further investigations introducing properties of ultrafilters in strong sense dual to being normal.

生成集的同构类

Isomorphism Classes of Generating Sets

本文研究生成集的同构类，通过构造超滤子，证明在特定偏序下存在同构的超滤子结构，并探讨超滤子的Tukey型性质。

违反广义连续统假设的度量

Measures that violate the Generalized Continuum Hypothesis

研究了在正则基数上存在简单P_λ-点超滤子的条件，并证明了其与多个基数的等价关系，同时改进了致密性强度下界并探讨了相关数学结构的保测性及滤子游戏的变化。