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Elementary point about measurable cards

  1. Jul 29, 2014 #1
    Just refreshing my understanding of measurable cardinals, the first step (more questions may follow, but one step at a time) is to make sure I understand the conditions: one of them is

    For a (an uncountable) measurable cardinal κ, there exists a non-trivial, 0-1-valued measure μ on P(κ) such that there exists an λ<κ such that for any sequence [Aα: α<λ ] of disjoint sets Aα whose elements are smaller-than-κ ordinals, μ([itex]\cup[/itex]{ Aα }) = ∑μ(Aα)

    Would not this mean that there would be a β<λ such that μ(Aβ) = 1 and [itex]\forall[/itex]γ<λ, (γ≠ β [itex]\Rightarrow[/itex] μ(Aβ) = 0)?

    If not, why not?

    P.S. except of course for those sequences for which for all α in the set of indices of the sequence, μ(Aα)=0
     
    Last edited: Jul 29, 2014
  2. jcsd
  3. Aug 3, 2014 #2
    I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?
     
  4. Aug 3, 2014 #3

    mathman

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    "measurable cardinal" is an extremely specialized concept. I am not surprised as the lack of response. I had to look it up on Wikipedia to get an inkling of what means.
     
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