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On tree ideals
Let 10 and m0 be the ideals associated with Laver and Miller forcing, respectively. We show that add(l0) < cov(10) and add(mO) < cov(mO) are consistent. We also show that both Laver and Miller
Analytic countably splitting families
  • O. Spinas
  • Mathematics
    Journal of Symbolic Logic
  • 1 March 2004
A notion of a splitting tree is defined, by means of which it is proved that every analytic countable splitting family contains a closed countably splitting family.
Uniformity of the Meager Ideal and Maximal Cofinitary Groups
Abstract We prove that every maximal cofinitary group has size at least the cardinality of the smallest non-meager set of reals. We also provide a consistency result saying that the spectrum of
Independence and Consistency Proofs in Quadratic Form Theory
These properties have been considered first in [G/O] in the process of investigating the orthogonal group of quadratic spaces, and it has been shown there (in ZFC) that over arbitrary uncountable fields (**)-spaces of unccountable dimension exist.
The distributivity numbers of finite products of P(ω)/fin
Generalizing [ShSp], for every n < ω we construct a ZFC-model where the distributivity number of r.o.(P(ω)/fin), h(n + 1), is smaller than the one of r.o.(P(ω)/fin). This answers an old problem of
The distributivity numbers of ()/fin and its square
We show that in a model obtained by forcing with a countable support iteration of Mathias forcing of length ω2, the distributivity number of P(ω)/fin is ω2, whereas the distributivity number of
Dominating and Unbounded Free Sets
It is proved that every analytic set in ω ω × ω⩽ with σ-bounded sections has a not ρbounded closed free set, and under projective determinacy analytic is replaced by projective.
Large cardinals and projective sets
From the same assumption plus a precipitous ideal, it is shown how a model can be forced where every $\Sigma ^1_{n+4}-$set is measurable and has Baire property.
On Gross Spaces
A Gross space is a vector space E of infinite dimension over some field F, which is endowed with a symmetric bilinear form � : E 2 → F and has the property that every infinite dimensional subspace U