Reduced powers of -trees
Reflection implies the SCH
We prove that, e.g., if μ > cf(μ) = ℵ₀ and and every stationary family of countable subsets of μ⁺ reflects in some subset of μ⁺ of cardinality ℵ₁, then the SCH for μ⁺ holds (moreover, for μ⁺, any scale for μ⁺ has a bad stationary set of cofinality ℵ₁). This answers a question of Foreman and Todorčević who get such a conclusion from the simultaneous reflection of four stationary sets.
Regular closure and corresponding versions of and
Relations d'équivalence co-analytiques
Relations impartibles [Book]
Remarks on cellularity in products
Remarks on chain conditions in products
Remarks on Pκλ-combinatorics
Remarks to a modification of Ramsey-type theorems
Riga -point
Rigid Aronszajn Trees
Rigid Aronszajn trees.
Rothberger gaps in fragmented ideals
The Rothberger number (ℐ) of a definable ideal ℐ on ω is the least cardinal κ such that there exists a Rothberger gap of type (ω,κ) in the quotient algebra (ω)/ℐ. We investigate (ℐ) for a class of ideals, the fragmented ideals, and prove that for some of these ideals, like the linear growth ideal, the Rothberger number is ℵ₁, while for others, like the polynomial growth ideal, it is above the additivity of measure. We also show that it is consistent that there are infinitely many (even continuum...
Selections on -spaces
We show that if is an uncountable AD (almost disjoint) family of subsets of then the space does not admit a continuous selection; moreover, if is maximal then does not even admit a continuous selection on pairs, answering thus questions of T. Nogura.
Selectivity of almost disjoint families
Semiproper ideals
We say that an ideal I on is semiproper if the corresponding poset is semiproper. In this paper we investigate properties of semiproper ideals on .
Separating collections
Set mappings on generalized linear continua
Set theoretical analogues of two combinatorial theorems
Set-theoretic characteristics of summability of sequences and convergence of series