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ON THE UNIQUENESS OF MEASURE AND CATEGORY σIDEALS ON 2ω
, 2006
"... Abstract. We prove that if a pair 〈I, J 〉 of ccc, translation invariant σideals on 2ω has the Fubini Property, then I = J. This leads to a slightly improved exposition of a part of the FarahZapletal proof of an invariant version of their theorem which characterizes the measure and category σideal ..."
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Abstract. We prove that if a pair 〈I, J 〉 of ccc, translation invariant σideals on 2ω has the Fubini Property, then I = J. This leads to a slightly improved exposition of a part of the FarahZapletal proof of an invariant version of their theorem which characterizes the measure and category σideals on 2ω as essentially the only ccc definable σideals with Fubini Property. 1.
A PARALLEL TO THE NULL IDEAL FOR INACCESSIBLE λ
, 2012
"... Abstract. It is well known to generalize the meagre ideal replacing ℵ0 by a (regular) cardinal λ> ℵ0 and requiring the ideal to be λ +complete. But can we generalize the null ideal? In terms of forcing, this means finding a forcing notion similar to the random real forcing, replacing ℵ0 by λ, so ..."
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Abstract. It is well known to generalize the meagre ideal replacing ℵ0 by a (regular) cardinal λ> ℵ0 and requiring the ideal to be λ +complete. But can we generalize the null ideal? In terms of forcing, this means finding a forcing notion similar to the random real forcing, replacing ℵ0 by λ, so requiring it to be (< λ)complete. Of course, we would welcome additional properties generalizing the ones of the random real forcing. Returning to the ideal (instead of forcing) we may look at the Boolean Algebra of λBorel sets modulo the ideal. Surprisingly we get a positive = existence answer for λ a “mild ” large cardinal: the weakly compact one. We apply this to get consistency results on cardinal invariants for such λ’s. We shall deal with other cardinals more properties related forcing notions in a continuation. (1004) revision:20120524 modified:20120528
CONSISTENTLY THERE IS NO NON TRIVIAL CCC FORCING NOTION WITH THE SACKS OR LAVER PROPERTY
, 2000
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SWEET & SOUR AND OTHER FLAVOURS OF CCC FORCING NOTIONS
, 2001
"... We continue developing the general theory of forcing notions built with the use of norms on possibilities, this time concentrating on ccc forcing notions and classifying them. ..."
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We continue developing the general theory of forcing notions built with the use of norms on possibilities, this time concentrating on ccc forcing notions and classifying them.