# Combinatorial properties of the ideal

Jacek Cichon, Andrzej Roslanowski, Juris Steprans and Bogdan Weglorz

We investigate the ideal  of subsets A of the Cantor space  such that for every infinite set  the restriction  is a proper subset of 2T. We present several new results concerning cardinal invariants of the ideal. For example, we show that the covering number  (= the minimal size of a family of sets from the ideal covering the whole space) of this ideal is not greater than the successor of the cofinality number (the minimal size of a basis) of the null ideal. A new property of forcing notions (New Set - New Function property) appears naturally in this context. The property seems to be a relative of weak distributivity (if looked at from the point of view of Boolean algebras).
Andrzej Roslanowski
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