Universal sets for ideals and the porosity thereof

Abstract We build a universal set in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msup> <m:mi>ω</m:mi> <m:mi>ω</m:mi> </m:msup> <m:mo>×</m:mo> <m:msup> <m:mn>2</m:mn> <m:mi>ω</m:mi> </m:msup> </m:mrow> </m:math> {\omega^{\omega}\times 2^{\omega}} for the family of summable ideals. We investigate its Borel complexity and topological properties, such as meagerness and σ-porosity.