This survey is motivated by specific questions arising in the similarities and contrasts
between (Baire) category and (Lebesgue) measure—category-measure duality and non …

We study maximal independent families (mif) in the projective hierarchy. We show that (a)
the existence of a $\boldsymbol {\Sigma}^ 1_2 $ mif is equivalent to the existence of a …

We show that there are no infinite maximal almost disjoint (“mad”) families in Solovay's
model, thus solving a long-standing problem posed by ARD Mathias in 1969. We also give a …

Given an uncountable cardinal $\kappa $, we consider the question of whether subsets of
the power set of $\kappa $ that are usually constructed with the help of the axiom of choice …

We prove the consistency of together with the existence of a-definable mad family,
answering a question posed by Friedman and Zdomskyy in [7, Question 16]. For the proof …

We develop a new forcing notion for adjoining self-coding cofinitary permutations and use it
to show that consistently, the minimal cardinality $\mathfrak a_ {\text {g}} $ of a maximal …

Mathematical Logic Page 1 Arch. Math. Logic (2013) 52:809–822 DOI 10.1007/s00153-013-0345-8
Mathematical Logic Co-analytic mad families and definable wellorders Vera Fischer · Sy David …

Let $\mathcal R $ be a $\Sigma^ 1_1 $ binary relation, and recall that a set $ A $ is
$\mathcal R $-discrete if no two elements of $ A $ are related by $\mathcal R $. We show …

We study the definability of maximal towers and of inextendible linearly ordered towers (ilt's),
a notion that is more general than that of a maximal tower. We show that there is, in the …

We consider maximal almost disjoint families of block subspaces of countable vector
spaces, focusing on questions of their size and definability. We prove that the minimum …