Locally-generic Boolean algebras and cardinal sequences
โ Scribed by Joan Bagaria
- Publisher
- Springer
- Year
- 2002
- Tongue
- English
- Weight
- 330 KB
- Volume
- 47
- Category
- Article
- ISSN
- 0002-5240
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๐ SIMILAR VOLUMES
Lct 1 be an infinite cardinal and let A , B be Boolean algebras. A homomorphism h: , 4 4 B is said to be A-cmpkte if whenever X is a subset of A of cardinality I such that the join V X of X exists in A , then V h[X] exists in B and is equal to h(V X ) . If x is an infinite cardinal, B is said to be
## Abstract For an infinite cardinal __K__ a stronger version of __K__โdistributivity for Boolean algebras, called kโpartition completeness, is defined and investigated (e. g. every __K__โSuslin algebra is a __K__โpartition complete Boolean algebra). It is shown that every __k__โpartition complete
We prove that if GCH holds and ฯ = ฮบฮฑ : ฮฑ < ฮท is a sequence of infinite cardinals such that ฮบฮฑ โฅ |ฮท| for each ฮฑ < ฮท, then there is a cardinal-preserving partial order that forces the existence of a scattered Boolean space whose cardinal sequence is ฯ .