arXiv subjects

Sakae Fuchino

Publications and source records attributed to Sakae Fuchino.

4 recordsLinked to original sources

arXiv2003

Remarks on a paper by Juhász and Kunen

We give an equivalent, but simpler formulation of the axiom SEP introduced by Juhasz and Kunen. Our formulation shows that many of the consequences of the weak Freese-Nation Property of $\mathcal P(ω)$ already follow from SEP. We show that it is consistent that SEP holds while $\mathcal P(ω)$ fails to have the $(\aleph_1,\aleph_0)$-ideal property, which has been introduced by Hart and Dow . This answers a question addressed independently by Fuchino and by Kunen. We also consider some natural variants of SEP and show that certain changes in the definition of SEP do not lead to a different principle. This answers a question addressed by Blass.

math.LO↗

arXiv1999

On absolutely divergent series

We show that in the aleph_2-stage countable support iteration of Mathias forcing over a model of CH the complete Boolean algebra generated by absolutely divergent series under eventual dominance is not isomorphic to the completion of P(omega)/fin. This complements Vojtas' result, that under cf(c)=p the two algebras are isomorphic

math.LO↗

arXiv1997

Coloring ordinals by reals

We introduce several new set-theoretic axioms formulated in terms of coloring of ordinals by reals. We show that these axioms generalize the axioms considered by I.Juhasz, L.Soukup and Z.Szentmiklossy, and give a class of p.o.s including Cohen p.o.-sets which force the axioms. In appearance these axioms are somewhat similar to OCA but it appears that they are inconsistent with OCA.

math.LO↗

arXiv1996

More Set-theory around the weak Freese-Nation property

In this paper, we introduce a very weak square principle which is even weaker than the similar principle introduced by Foreman and Magidor. A characterization of this principle is given in term of sequences of elementary submodels of H(χ). This is used in turn to prove a characterization of kappa-Freese-Nation property under the very weak square principle and a weak variant of the Singular Cardinals Hypothesis. A typical application of this characterization shows that under 2^{\aleph_0}<\aleph_ωand our very weak square for \aleph_ω, the partial ordering [omega_ω]^{<ω} (ordered by inclusion) has the aleph_1-Freese-Nation property. On the other hand we show that, under Chang's Conjecture for \aleph_ωthe partial ordering above does not have the aleph_1-Freese-Nation property. Hence we obtain the independence of our characterization of the kappa-Freese-Nation property and also of the very weak square principle from ZFC.

math.LO↗