Definable Davies' theorem
We prove the following descriptive set-theoretic analogue of a theorem of R. O. Davies: Every Σ¹₂ function f:ℝ × ℝ → ℝ can be represented as a sum of rectangular Σ¹₂ functions if and only if all reals are constructible.
Template iterations and maximal cofinitary groups
Jörg Brendle (2003) used Hechler’s forcing notion for adding a maximal almost disjoint family along an appropriate template forcing construction to show that (the minimal size of a maximal almost disjoint family) can be of countable cofinality. The main result of the present paper is that , the minimal size of a maximal cofinitary group, can be of countable cofinality. To prove this we define a natural poset for adding a maximal cofinitary group of a given cardinality, which enjoys certain combinatorial...
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