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In set theory, Cichoń's diagram or Cichon's diagram is a table of 10 infinite cardinal numbers related to the set theory of the reals displaying the provable relations between these cardinal characteristics of the continuum. All these cardinals are greater than or equal to , the smallest uncountable cardinal, and they are bounded above by , the cardinality of the continuum. Four cardinals describe properties of the ideal of sets of measure zero; four more describe the corresponding properties of the ideal of meager sets (first category sets). ==Definitions== Let ''I'' be an ideal of a fixed infinite set ''X'', containing all finite subsets of ''X''. We define the following "cardinal coefficients" of ''I'': *. ::The "additivity" of ''I'' is the smallest number of sets from ''I'' whose union is not in ''I'' any more. As any ideal is closed under finite unions, this number is always at least ; if ''I'' is a σ-ideal, then add(''I'')≥. *. :: The "covering number" of ''I'' is the smallest number of sets from ''I'' whose union is all of ''X''. As ''X'' itself is not in ''I'', we must have add(''I'') ≤ cov(''I''). *, :: The "uniformity number" of ''I'' (sometimes also written ) is the size of the smallest set not in ''I''. By our assumption on ''I'', add(''I'') ≤ non(''I''). * :: The "cofinality" of ''I'' is the cofinality of the partial order (''I'', ⊆). It is easy to see that we must have non(''I'') ≤ cof(''I'') and cov(''I'') ≤ cof(''I''). Furthermore, the "bounding number" or "unboundedness number" and the "dominating number" are defined as follows: * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Cichoń's diagram」の詳細全文を読む スポンサード リンク
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