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3 Fundamenta Mathematicae

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Perfect set theorems

100%

Spinas O.

tom 201

nr 2

179-195

We study splitting, infinitely often equal (ioe) and refining families from the descriptive point of view, i.e. we try to characterize closed, Borel or analytic such families by proving perfect set theorems. We succeed for $G_{δ}$ hereditary splitting families and for analytic countably ioe families. We construct several examples of small closed ioe and refining families.

The distributivity numbers of finite products of P(ω)/fin

63%

Shelah S. , Spinas O.

Fundamenta Mathematicae

1998

tom 158

nr 1

81-93

Generalizing [ShSp], for every n < ω we construct a ZFC-model where ℌ(n), the distributivity number of r.o.$(P(ω)/fin)^n$, is greater than ℌ(n+1). This answers an old problem of Balcar, Pelant and Simon (see [BaPeSi]). We also show that both Laver and Miller forcings collapse the continuum to ℌ(n) for every n < ω, hence by the first result, consistently they collapse it below ℌ(n).

Linear topologies on sesquilinear spaces of uncountable dimension

44%

Spinas O.

Fundamenta Mathematicae

1991

tom 139

nr 2

119-132