On the complexity of Hamel bases of infinite dimensional Banach spaces

We call a subset S of a topological vector space V linearly Borel, if for every finite number n, the set of all linear combinations of S of length n is a Borel subset of V. It will be shown that a Hamel base of an infinite dimensional Banach space can never be linearly Borel. This answers a question of Anatolij Plichko

Taiwan`s domestic politics since the presidential elections 2000

This paper looks at several developments that have taken place in domestic politics on Taiwan since the election of Chen Shui-bian as president of the Republic of China on Taiwan in 1998. After discussing the political successes and failures of the incumbent Chen administration, it analyses its strategy in dealing with the consequences of divided government. Some of the problems encountered by the administration are traced to changes in the political system of Taiwan that took place during the presidency of Lee Teng-hui. The paper also deals with the new role of the president as chief executive and functioning of the legislative. Finally, the reaction of the major political parties to the changes in the political situation is explored. --Taiwan,domestic politics,divided government,political system,party system,Chen Shui-bian,Lee Teng-hui

Ramseyan ultrafilters

We investigate families of partitions of omega which are related to special coideals, so-called happy families, and give a dual form of Ramsey ultrafilters in terms of partitions. The combinatorial properties of these partition-ultrafilters, which we call Ramseyan ultrafilters, are similar to those of Ramsey ultrafilters. For example it will be shown that dual Mathias forcing restricted to a Ramseyan ultrafilter has the same features as Mathias forcing restricted to a Ramsey ultrafilter. Further we introduce an ordering on the set of partition-filters and consider the dual form of some cardinal characteristics of the continuum

Consequences of arithmetic for set theory

In this paper, we consider certain cardinals in ZF (set theory without AC, the Axiom of Choice). In ZFC (set theory with AC), given any cardinals C and D, either C <= D or D <= C. However, in ZF this is no longer so. For a given infinite set A consider Seq(A), the set of all sequences of A without repetition. We compare |Seq(A)|, the cardinality of this set, to |P(A)|, the cardinality of the power set of A. What is provable about these two cardinals in ZF? The main result of this paper is that ZF |- for all A: |Seq(A)| not= |P(A)| and we show that this is the best possible result. Furthermore, it is provable in ZF that if B is an infinite set, then |fin(B)|<|P(B)|, even though the existence for some infinite set B^* of a function f from fin(B^*) onto P(B^*) is consistent with ZF

Techniques for approaching the dual Ramsey property in the projective hierarchy

We define the dualizations of objects and concepts which are essential for investigating the Ramsey property in the first levels of the projective hierarchy, prove a forcing equivalence theorem for dual Mathias forcing and dual Laver forcing, and show that the Harrington-Kechris techniques for proving the Ramsey property from determinacy work in the dualized case as well

Ultrafilter spaces on the semilattice of partitions

The Stone-Cech compactification of the natural numbers bN, or equivalently, the space of ultrafilters on the subsets of omega, is a well-studied space with interesting properties. If one replaces the subsets of omega by partitions of omega, one can define corresponding, non-homeomorphic spaces of partition ultrafilters. It will be shown that these spaces still have some of the nice properties of bN, even though none is homeomorphic to bN. Further, in a particular space, the minimal height of a tree pi-base and P-points are investigated

Relations between some cardinals in the absence of the Axiom of Choice

If we assume the axiom of choice, then every two cardinal numbers are comparable. In the absence of the axiom of choice, this is no longer so. For a few cardinalities related to an arbitrary infinite set, we will give all the possible relationships between them, where possible means that the relationship is consistent with the axioms of set theory. Further we investigate the relationships between some other cardinal numbers in specific permutation models and give some results provable without using the axiom of choice