TY - JOUR
T1 - On ultraproducts of Boolean algebras and irr
AU - Shelah, Saharon
PY - 2003/8
Y1 - 2003/8
N2 - § 1. Consistent inequality [We prove the consistency of irr(∏ i Bi/D) < ∏i irr(B i)/D where D is an ultrafilter on K and each Bi is a Boolean algebra and irr(B) is the maximal size of irredundant subsets of a Boolean algebra B, see full definition in the text. This solves the last problem, 35, of this form from Monk's list of problems in [M2]. The solution applies to many other properties, e.g. Souslinity.] § 2. Consistency for small cardinals [We get similar results with K = א1 (easily we cannot have it for K = א0) and Boolean algebras Bi (i < K) of cardinality < ω1.] This article continues Magidor Shelah [MgSh 433] and Shelah Spinas [ShSi 677], but does not rely on them: see [M2] for the background.
AB - § 1. Consistent inequality [We prove the consistency of irr(∏ i Bi/D) < ∏i irr(B i)/D where D is an ultrafilter on K and each Bi is a Boolean algebra and irr(B) is the maximal size of irredundant subsets of a Boolean algebra B, see full definition in the text. This solves the last problem, 35, of this form from Monk's list of problems in [M2]. The solution applies to many other properties, e.g. Souslinity.] § 2. Consistency for small cardinals [We get similar results with K = א1 (easily we cannot have it for K = א0) and Boolean algebras Bi (i < K) of cardinality < ω1.] This article continues Magidor Shelah [MgSh 433] and Shelah Spinas [ShSi 677], but does not rely on them: see [M2] for the background.
UR - http://www.scopus.com/inward/record.url?scp=0041917188&partnerID=8YFLogxK
U2 - 10.1007/s00153-002-0167-6
DO - 10.1007/s00153-002-0167-6
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AN - SCOPUS:0041917188
SN - 0933-5846
VL - 42
SP - 569
EP - 581
JO - Archive for Mathematical Logic
JF - Archive for Mathematical Logic
IS - 6
ER -