# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## MAD families with strong combinatorial properties

### Tom 193 / 2007

Fundamenta Mathematicae 193 (2007), 7-21 MSC: Primary 03E50; Secondary 03E05, 03E15, 03E40. DOI: 10.4064/fm193-1-2

#### Streszczenie

In his paper in Fund. Math. 178 (2003), Miller presented two conjectures regarding MAD families. The first is that CH implies the existence of a MAD family that is also a $\sigma$-set. The second is that under CH, there is a MAD family concentrated on a countable subset. These are proved in the present paper.

#### Autorzy

• Jörg BrendleThe Graduate School of Science and Technology
Kobe University
Kobe 657-8501, Japan
e-mail
• Greg PiperThe Graduate School of Science and Technology
Kobe University