几个特殊的序超滤子

Ordinal ultrafilters versus P-hierarchy

An earlier paper, entitled "P-hierarchy on $βω$", investigated the relations between ordinal ultrafilters and the so-called P-hierarchy. This study is continued in the present paper and focuses on the aspects of characterization of classes of finite index, existence, generic existence and the Rudin-Keisler-order.

Euclidean integers, Euclidean ultrafilters, and Euclidean numerosities

We introduce axiomatically the ring $\bf{Z}_κ$ of the Euclidean integers, that can be viewed as the ``integral part" of the field $\mathbb{E}$ of Euclidean numbers of [4], where the transfinite sum of ordinal indexed $κ$-sequences of integers is well defined. In particular any ordinal might be identified with the transfiite sum of its characteristic function, preserving the so called natural operations. The ordered ring $\bf{Z}_κ$ may be obtained as an ultrapower of $\mathbb{Z}$ modulo suitable ultrafilters, thus constituting a \it{ring of nonstandard integers.} Most relevant is the \it{algebr…

How high can Baumgartner's {\cal I}-ultrafilters lie in the P-hierarchy?

Under CH we prove that for any tall ideal $\cal I$ on $ω$ and for any ordinal $γ\leq ω_1$ there is an ${\cal I}$-ultrafilter (in the sense of Baumgartner), which belongs to the class ${\cal P}_γ$ of P-hierarchy of ultrafilters. Since the class of ${\cal P}_2$ ultrafilters coincides with a class of P-points, out result generalize theorem of Flašková, which states that there are ${\cal I}$-ultrafilters which are not P-points.

Spectra of uniformity

We study some limitations and possible occurrences of uniform ultrafilters on ordinals without the axiom of choice. We prove an Easton-like theorem about the possible spectrum of successors of regular cardinals which carry uniform ultrafilters; we also show that this spectrum is not necessarily closed.

Shelah 超滤子

Shelah Ultrafilters

本文研究了Shelah超滤子，证明了其可通过特殊forcing添加，并在多个Borel理想中表现为I-超滤子。

The seed order

We study various orders on countably complete ultrafilters on ordinals that coincide and are wellorders under a hypothesis called the Ultrapower Axiom. Our main focus is on the relationship between the Ultrapower Axiom and the linearity of these orders.