arXiv subjects

Avner Landver

Publications and source records attributed to Avner Landver.

3 recordsLinked to original sources

arXiv1992

Reflection and Weakly Collectionwise Hausdorff Spaces

We show that square(theta) implies that there is a first countable <theta-collectionwise Hausdorff space that is not weakly theta-collectionwise Hausdorff. We also show that in the model obtained by Levy collapsing a weakly compact (supercompact) cardinal to omega_2, first countable aleph_1-collectionwise Hausdorff spaces are weakly aleph_2-collectionwise Hausdorff (weakly collectionwise Hausdorff). In the last section we show that assuming E^omega_theta, a certain theta-family of integer valued functions exists and that in the model obtained by Levy collapsing a supercompact cardinal to omega_2, these families do not exist.

math.LO↗

arXiv1992

Finite Combinations of Baire Numbers

Let $κ$ be a regular cardinal. Consider the Baire numbers of the spaces $(2^θ)_κ$ (functions from $θ$ to 2 and the less than $κ$ topology) for various $θ\geq κ$. Let l be the number of such different Baire numbers. Models of set theory with l=1 or l=2 are known and it is also known that l is finite. We show here that if $κ> ω$, then l could be any given finite number. We do not know whether the same is true for $κ= ω$.

math.LO↗

arXiv1992

Remark on the Failure of Martin's Axiom

Let m be the least cardinal k such that MA(k) fails. The only known model for "m is singular" was constructed by Kunen. In Kunen's model cof(m)=omega_1. It is unknown whether "omega_1 < cof(m) < m" is consistent. The purpose of this paper is to present a proof of Kunen's result and to identify the difficulties of generalizing this result to an arbitrary uncountable cofinality.

math.LO↗