# A Sacks-indestructible partion of Baire space into compact sets II

11.10.2022 15:00 - 16:30

L. Schembecker (U Wien)

Remember that maximal almost disjoint families of finitely splitting trees (a.d.f.s. families) are in one-to-one correspondence with partitions of Baire space into compact sets. In part I we saw how to construct an a.d.f.s. family which is indestructible by the product of Sacks forcing of size \(\aleph_0\). In part II we strengthen the construction to get an a.d.f.s family which stays maximal after forcing with countably supported product or iteration of Sacks forcing of any length. The proof is an adaptation of the construction of a Sacks-indestructible maximal eventually different family by V. Fischer and D. Schrittesser. If time permits we give an idea how to generalize the construction to other combinatorial families, for example maximal cofinitary groups.

Students at Uni Wien are required to attend in person.

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#### SR 10, 1. Stock, Koling. 14-16, 1090 Wien

SR 10, 1. Stock, Koling. 14-16, 1090 Wien