منابع مشابه
Superatomic Boolean algebras: Maximal rigidity
We prove that for any superatomic Boolean Algebra of cardinality > i4 there is an automorphism moving uncountably many atoms. Similarly for larger cardinals. Any of those results are essentially best possible
متن کاملSuperatomic Boolean Algebras Constructed from Morasses
By using the notion of a simplified (n, 1)-morass, we construct n-thin-tall, K-thin-thick and, in a forcing extension, K-very thin-thick superatomic Boolean algebras for every infinite regular cardinal n.
متن کاملHeight and Width of Superatomic Boolean Algebras
Cantor-Bendixson height and width of superatomic Boolean algebras is investigated and it is shown that (1) you don't need a Canadian tree to construct an u>,-thin-thick superatomic Boolean algebra; (2) c can be very large and for all k < c and all uncountable X, k < c, there are no K-thin-very tall, X-thin-tall, ic-very thin-thick, or X-thin-thick superatomic Boolean algebras on k. 0. Introduct...
متن کاملOn Tightness and Depth in Superatomic Boolean Algebras
We introduce a large cardinal property which is consistent with L and show that for every superatomic Boolean algebra B and every cardinal λ with the large cardinal property, if tightness+(B) ≥ λ+, then depth(B) ≥ λ. This improves a theorem of Dow and Monk. In [DM, Theorem C], Dow and Monk have shown that if λ is a Ramsey cardinal (see [J, p.328]), then every superatomic Boolean algebra with ti...
متن کاملSuperatomic Boolean algebras constructed from strongly unbounded functions
Using Koszmider’s strongly unbounded functions, we show the following consistency result: Suppose that κ, λ are infinite cardinals such that κ ≤ λ, κ = κ and 2 = κ, and η is an ordinal with κ ≤ η < κ and cf(η) = κ. Then, in some cardinal-preserving generic extension there is a superatomic Boolean algebra B such that ht(B) = η + 1, wdα(B) = κ for every α < η and wdη(B) = λ (i.e. there is a local...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1967
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1967.23.479