منابع مشابه
Measurable cardinals and category bases
We show that the existence of a non-trivial category base on a set of regular cardinality with each subset being Baire is equiconsistent to the existence of a measurable cardinal.
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Say that κ’s measurability is destructible if there exists a <κ-closed forcing adding a new subset of κ which destroys κ’s measurability. For any δ, let λδ =df The least beth fixed point above δ. Suppose that κ is indestructibly supercompact and there is a measurable cardinal λ > κ. It then follows that A1 = {δ < κ | δ is measurable, δ is not a limit of measurable cardinals, δ is not δ+ strongl...
متن کاملBasic Facts about Inaccessible and Measurable Cardinals
Let X be an infinite set. One can check that X is infinite. The scheme ElemProp deals with a non empty set A , a set B, and a unary predicate P , and states that: P [B] provided the parameters meet the following requirement: • B ∈ {y;y ranges over elements of A : P [y]}. For simplicity, we use the following convention: N is a cardinal number, M is an aleph, X is a non empty set, Y , Z, Z1, Z2, ...
متن کاملMeasurable cardinals and the reals of L
• At stage 0, M0 = M , U0 = U and κ0 = κ. • At stage α+1, if it is well-founded, we build Ult(Mα, Uα) and let Mα+1 be its transitive collapse, where the ultrapower is computed from the point of view of Mα. Let jα,α+1 : Mα → Mα+1 be the ultrapower embedding. Then set κα+1 = j(κα) and Uα+1 = j(Uα). • At limit stages λ, if it is well-founded, we define Mλ as the direct limit of the directed system...
متن کاملSome Remarks on Real-valued Measurable Cardinals
We consider the set [u>]u and the cofinality of the set KX assuming that some cardinals are endowed in total measures. Introduction. A cardinal k is real-valued measurable if there exists a /ccomplete atomless probability measure on P(k), the set of all subsets of the cardinal /c. The status and the philosophy concerned e.g. real-valued measurable cardinals have been detailed and presented in a...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2017
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2017.05.006