## Application of base tree theorem.(English)Zbl 0978.03036

The authors study ideals $${\mathcal K}^\kappa$$, where $$2\leq \kappa\leq {\mathfrak c}$$ is a cardinal, on $$[\omega]^\omega$$, which are defined as follows: For a maximal almost disjoint (MAD) family $$\mathcal A$$, let $$J^\kappa({\mathcal A})$$ be the set of all $$X\in[\omega]^\omega$$ which meet at least $$\kappa$$ elements of $$\mathcal A$$ infinitely often. Then $${\mathcal K}^\kappa$$ is the ideal generated by all sets $$J^\kappa({\mathcal A})$$, where $$\mathcal A$$ is a MAD family. Among other things, the additivity, covering and cofinality numbers of these ideals are studied. Also, the solution to a question of Hechler is given.

### MSC:

 300000 Other combinatorial set theory 3e+17 Cardinal characteristics of the continuum
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