arXiv subjects

Yasuo Yoshinobu

Publications and source records attributed to Yasuo Yoshinobu.

7 recordsLinked to original sources

arXiv2026

Convex sets and Axiom of Choice

Under $\mathrm{ZF}$, we show that the statement that every subset of every $\mathbb{R}$-vector space has a maximal convex subset is equivalent to the Axiom of Choice. We also study the strength of the same statement restricted to some specific $\mathbb{R}$-vector spaces. In particular, we show that the statement for $\mathbb{R}^2$ is equivalent to the Axiom of Countable Choice for reals, whereas the statement for $\mathbb{R}^3$ is equivalent to the Axiom of Uniformization. We discuss the statement for some spaces of higher dimensions as well.

math.LO↗

arXiv2026

More on setwise climbability properties

We introduce two types of variations of setwise climbability properties, which have been introduced by the second author as fragments of Jensen's square principles. We show that variations of the first type are equivalent to known principles and that they are consistent with the Proper Forcing Axiom(PFA). On the other hand, those of the second type can be characterized as Martin-type axioms for some classes of posets defined in terms of a new variation of generalized Banach-Mazur games, and they are no longer consistent with PFA. We also study how large fragments of PFA are consistent with these principles.

math.LO↗

arXiv2019

Properness under closed forcing

For every uncountable regular $κ$, we give two examples of proper posets which turn improper in some $κ$-closed forcing extension.

math.LO↗

arXiv2017

The *-variation of the Banach-Mazur game and forcing axioms

We introduce a property of posets which strengthens (ω_1+1)-strategic closedness. This property is defined using a variation of the Banach-Mazur game on posets, where the first player chooses a countable set of conditions instead of a single condition at each turn. We prove PFA is preserved under any forcing over a poset with this property. As an application we reproduce a proof of Magidor's theorem about the consistency of PFA with some weak variations of the square principles. We also argue how different this property is from (ω_1+1)-operational closedness, which we introduced in our previous work, by observing which portions of MA^+(ω_1-closed) are preserved or destroyed under forcing over posets with either property.

math.LO↗

arXiv2006

Kurepa-trees and Namba-forcing

We show that compact cardinals and {\rm MM} are sensitive to $λ$-closed forcings for arbitrarily large $λ$. This is done by adding 'regressive' $λ$-Kurepa-trees in either case. We argue that the destruction of regressive Kurepa-trees with {\rm MM} requires the use of Namba forcing.

math.LO↗

arXiv2006

How many miles to beta-X? -- d miles, or just one foot

It is known that the Stone-Cech compactification of a metrizable space X is approximated by the collection of Smirnov compactifications of X for all compatible metrics on X. If we confine ourselves to locally compact separable metrizable spaces, the corresponding statement holds for Higson compactifications. We investigate the smallest cardinality of a set D of compatible metrics on X such that the Stone-Cech compactification of X is approximated by Smirnov or Higson compactifications for all metrics in D. We prove that it is either the dominating number or 1 for a locally compact separable metrizable space.

math.GN↗

arXiv2004

How many miles to $βω$? -- Approximating $βω$ by metric-dependent compactifications

It is known that the Stone-Čech compactification of a non-compact metrizable space $X$ is approximated by the collection of Smirnov compactifications of $X$ for all compatible metrics on $X$. We investigate the smallest cardinality of a set $D$ of compatible metrics on the countable discrete space $ω$ such that, the Stone-Čech compactification of $ω$ is approximated by Smirnov compactifications for all metrics in $D$, but any finite subset of $D$ does not suffice. We also study the corresponding cardinality for Higson compactifications.

math.GN↗