36 research outputs found
Covering a bounded set of functions by an increasing chain of slaloms
A slalom is a sequence of finite sets of length omega. Slaloms are ordered by
coordinatewise inclusion with finitely many exceptions. Improving earlier
results of Mildenberger, Shelah and Tsaban, we prove consistency results
concerning existence and non-existence of an increasing sequence of a certain
type of slaloms which covers a bounded set of functions in the Baire space
Pcf theory and cardinal invariants of the reals
The additivity spectrum ADD(I) of an ideal I is the set of all regular
cardinals kappa such that there is an increasing chain {A_alpha:alpha<kappa\}
in the ideal I such that the union of the chain is not in I.
We investigate which set A of regular cardinals can be the additivity
spectrum of certain ideals.
Assume that I=B or I=N, where B denotes the sigma-ideal generated by the
compact subsets of the Baire space omega^omega, and N is the ideal of the null
sets.
For countable sets we give a full characterization of the additivity spectrum
of I: a non-empty countable set A of uncountable regular cardinals can be
ADD(I) in some c.c.c generic extension iff A=pcf(A).Comment: 9 page
Preservation of a Convergence of a Sequence to a Set
We say that a sequence of points converges to a set if every open set containing the set contains all but finitely many terms of the sequence. We investigate preservation of convergence of a sequence to a set in forcing extensions