The approachability ideal without a maximal set

A relative of the approachability ideal, diamond and non-saturation

Some Consequences of Reflection on the Approachability Ideal

We study the approachability ideal I[κ+] in the context of large cardinals and properties of the regular cardinals below a singular κ. As a guiding example consider the approachability ideal I[אω+1] assuming that אω is a strong limit. In this case we obtain that club many points in אω+1 of cofinality אn for some n > 1 are approachable assuming the joint reflection of countable families of stati...

The Maximal Regular Ideal of a Ring

Set-valued approachability and online learning with partial monitoring

Approachability has become a standard tool in analyzing learning algorithms in the adversarial online learning setup. We develop a variant of approachability for games where there is ambiguity in the obtained reward: it belongs to a set rather than being a single vector. Using this variant we tackle the problem of approachability in games with partial monitoring and develop a simple and general...

Maximal irredundance and maximal ideal independence in Boolean algebras