38 research outputs found
Superatomic Boolean algebras constructed from strongly unbounded functions
Using Koszmider's strongly unbounded functions, we show the following
consistency result:
Suppose that are infinite cardinals such that , and , and
is an ordinal with and .
Then, in some cardinal-preserving generic extension there is a superatomic
Boolean algebra such that - , - the cardinality of the
th level of is for every , - and the
cardinality of the th level of is Especially,
\_{{\omega}_1}\concatenation \$ and
\_{{\omega}_2}\concatenation \$ can be cardinal
sequences of superatomic Boolean algebras.Comment: 13 page
On constructions with -cardinals
We propose developing the theory of consequences of morasses relevant in
mathematical applications in the language alternative to the usual one,
replacing commonly used structures by families of sets originating with
Velleman's neat simplified morasses called -cardinals. The theory of related
trees, gaps, colorings of pairs and forcing notions is reformulated and
sketched from a unifying point of view with the focus on the applicability to
constructions of mathematical structures like Boolean algebras, Banach spaces
or compact spaces.
A new result which we obtain as a side product is the consistency of the
existence of a function
with the
appropriate -version of property for regular
satisfying .Comment: Minor correction
Spectra of Tukey types of ultrafilters on Boolean algebras
Extending recent investigations on the structure of Tukey types of
ultrafilters on to Boolean algebras in general, we
classify the spectra of Tukey types of ultrafilters for several classes of
Boolean algebras, including interval algebras, tree algebras, and pseudo-tree
algebras.Comment: 18 page
Superatomic Boolean algebras constructed from strongly unbounded functions
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