O. Spinas

Publications53
h-index12
Citations338
Highly Influential Citations20
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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…
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Analytic countably splitting families
  • O. Spinas
  • Mathematics
    Journal of Symbolic Logic
  • 1 March 2004
TLDR
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.
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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…
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Independence and Consistency Proofs in Quadratic Form Theory
TLDR
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.
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Regularity Properties for Dominating Projective Sets
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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…
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Dominating and Unbounded Free Sets
TLDR
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.
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Large cardinals and projective sets
TLDR
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.
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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…
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