Searcharxiv⌕ Search

arXiv subjects

Jakob Kellner

Publications and source records attributed to Jakob Kellner.

25 records · Page 2Linked to original sources
arXiv2009

A Sacks Real out of Nowhere

There is a proper countable support iteration of length $ω$ adding no new reals at finite stages and adding a Sacks real in the limit.

math.LO↗
arXiv2008

Decisive creatures and large continuum

For $f,g\inω\ho$ let $\mycfa_{f,g}$ be the minimal number of uniform $g$-splitting trees needed to cover the uniform $f$-splitting tree, i.e. for every branch $ν$ of the $f$-tree, one of the $g$-trees contains $ν$. $\myc_{f,g}$ is the dual notion: For every branch $ν$, one of the $g$-trees guesses $ν(m)$ infinitely often. It is consistent that $\myc_{f_ε,g_ε}=\mycfa_{f_ε,g_ε}=κ_ε$ for $\al1$ many pairwise different cardinals $κ_ε$ and suitable pairs $(f_ε,g_ε)$. For the proof we use creatures with sufficient bigness and halving. We show that the lim-inf creature forcing satisfies fusion and pure decision. We introduce decisiveness and use it to construct a variant of the countable support iteration of such forcings, which still satisfies fusion and pure decision.

math.LO↗
arXiv2007

Winning the pressing down game but not Banach Mazur

Let $S$ be the set of those $α\inω_2$ that have cofinality $ω_1$. It is consistent relative to a measurable that the nonempty player wins the pressing down game of length $ω_1$, but not the Banach Mazur game of length $ω+1$ (both games starting with $S$).

math.LO↗
arXiv2005

Preserving Non-Null with Suslin+ forcing

We introduce the notion of effective Axiom A and use it to show that some popular tree forcings are Suslin+. We introduce transitive nep and present a simplified version of Shelah's "preserving a little implies preserving much": If I is a Suslin ccc ideal (e.g. Lebesgue-null or meager) and P is a transitive nep forcing (e.g. P is Suslin+) and P doesn't make any I-positive Borel set small, then P doesn't make any I-positive set small.

math.LO↗
arXiv2004

Preserving Preservation

We present preservation theorems for countable support iteration of nep forcing notions satisfying ``old reals are not Lebesgue null'' and ``old reals are not meager''. (Nep is a generalization of Suslin proper.) We also give some results for general Suslin ccc ideals.

math.LO↗