Ideals of the second category
Ideals which generalize (v 0)
Countable products of finite discrete spaces with more than one point and ideals generated by Marczewski-Burstin bases (assigned to trimmed trees) are examined, using machinery of base tree in the sense of B. Balcar and P. Simon. Applying Kulpa-Szymanski Theorem, we prove that the covering number equals to the additivity or the additivity plus for each of the ideals considered.
Idempotence de l'opération de souslin
Internally club and approachable for larger structures
We generalize the notion of a fat subset of a regular cardinal κ to a fat subset of , where κ ⊆ X. Suppose μ < κ, , and κ is supercompact. Then there is a generic extension in which κ = μ⁺⁺, and for all regular λ ≥ μ⁺⁺, there are stationarily many N in which are internally club but not internally approachable.
Intersection properties of partitions of a cardinal
It is consistent that there exists an ordered real closed field which is not hyper-real.