Generalizing [ShSp], for every n < ω we construct a ZFC-model where the distributivity number of r.o.(P(ω)/fin), h(n + 1), is smaller than the one of r.o.(P(ω)/fin). This answers an old problem of Balcar, Pelant and Simon (see [BaPeSi]). We also show that both of Laver and Miller forcing collapse the continuum to h(n) for every n < ω, hence by the first result, consistently they collapse it bel...

In the theory of Type Two Effectivity (Weihrauch 2000), computation on non-discrete spaces is performed by type two Turing machines, which compute with infinite words acting as names for elements of spaces. The connection between names and their associated elements is specified by a many-to-one relation called a representation. Such representations induce a topology on the named elements, namel...

We prove that the skeleton of a product of finitely many finite distributive lattices is isomorphic to the product of skeletons of its factors. Thus, it is possible to construct finite distributive lattices with a given directly reducible skeleton by reducing the problem to the skeleton factors. Although not all possible lattices can be obtained this way, we show that it works for the smallest ...

Bacteriocins produced by lactic acid bacteria (LAB) are well-recognized for their potential as natural food preservatives. These antimicrobial peptides usually do not change the sensorial properties of food products and can be used in combination with traditional preservation methods to ensure microbial stability. In recent years, fruit products are increasingly being associated with food-borne...

σn(Γ) = {x ∈ {0, 1} Γ : |supp(x)| ≤ n}. Here supp(x) = {γ ∈ Γ : xγ 6= 0}. This is a closed, hence compact subset of {0, 1}, which is identified with the family of all subsets of Γ of cardinality at most n. In this work we will study the spaces which are countable products of spaces σn(Γ), mainly their topological classification as well as the classification of their Banach spaces of continuous ...