S1-paracompactness with respect to an ideal
... τ −codense if I ∩ τ = {∅}, that is, each member of I has empty τ −interior. An ideal I is completely codense [10] if I ⊂ N where N is the ideal of nowhere dense subsets in (X, τ ). An ideal I is said to be weakly τ −local [14] if A? = ∅ implies A ∈ I. I is called τ −locally finite [12] if the union ...
... τ −codense if I ∩ τ = {∅}, that is, each member of I has empty τ −interior. An ideal I is completely codense [10] if I ⊂ N where N is the ideal of nowhere dense subsets in (X, τ ). An ideal I is said to be weakly τ −local [14] if A? = ∅ implies A ∈ I. I is called τ −locally finite [12] if the union ...
Notes from the Prague Set Theory seminar
... 3.21 Example. Farah has an ideal I which is Ramsey and not semiselective and not ω-distributive. We will improve it so that it is (ω, 2)-distributive and P I . For u ∈ <ω R we define Au ⊆ ω such that A∅ = ω and {Aua ξ : ξ ∈ R} is a MAD on Au . Let H consist of all A ⊆ ω which have some Au ⊆∗ A. If w ...
... 3.21 Example. Farah has an ideal I which is Ramsey and not semiselective and not ω-distributive. We will improve it so that it is (ω, 2)-distributive and P I . For u ∈ <ω R we define Au ⊆ ω such that A∅ = ω and {Aua ξ : ξ ∈ R} is a MAD on Au . Let H consist of all A ⊆ ω which have some Au ⊆∗ A. If w ...
