arXiv subjects

Sakaé Fuchino

Publications and source records attributed to Sakaé Fuchino.

22 records · Page 2Linked to original sources

arXiv1998

Sticks and clubs

We study combinatorial principles known as stick and club. Several variants of these principles and cardinal invariants connected to them are also considered. We introduce a new kind of side-by-side product of partial orders which we call pseudo-product. Using such products, we give several generic extensions where some of these principles hold together with not CH and Martin's Axiom for countable p.o.-sets. An iterative version of the pseudo-product is used under an inaccessible cardinal to show the consistency of the club principle for every stationary subset of limits of omega_1 together with not CH and Martin's Axiom for countable p.o.-sets.

math.LO↗

arXiv1995

Partial orderings with the weak Freese-Nation property

A partial ordering P is said to have the weak Freese-Nation property (WFN) if there is a mapping f:P ---> [P]^{<= aleph_0} such that, for any a, b in P, if a <= b then there exists c in f(a) cap f(b) such that a <= c <= b. In this note, we study the WFN and some of its generalizations. Some features of the class of BAs with the WFN seem to be quite sensitive to additional axioms of set theory: e.g., under CH, every ccc cBA has this property while, under b >= aleph_2, there exists no cBA with the WFN.

math.LO↗

arXiv1995

A game on partial orderings

We study the determinacy of the game G_kappa (A) introduced in [FKSh:549] for uncountable regular kappa and several classes of partial orderings A. Among trees or Boolean algebras, we can always find an A such that G_kappa (A) is undetermined. For the class of linear orders, the existence of such A depends on the size of kappa^{< kappa}. In particular we obtain a characterization of kappa^{< kappa}= kappa in terms of determinacy of the game G_kappa (L) for linear orders L .

math.LO↗

arXiv1994

On a theorem of Shapiro

We show that a theorem of Leonid B. Shapiro which was proved under MA, is actually independent from ZFC. We also give a direct proof of the Boolean algebra version of the theorem under MA(Cohen).

math.LO↗