Two _{} ideals

TL;DR: This is a survey paper on the descriptive set theory of hereditary families of closed sets in Polish spaces and its applications to ideals and σ-ideals of closed or compact sets.

TL;DR: In this paper, the Furstenberg's, Golomb's, and Kirch's topologies were investigated, and it was shown that each of them has a topological representation and cannot be extended to a summable ideal.

TL;DR: In this paper, it was shown that if G is a filter with the Baire property and F is an analytic, non-countably generated p-filter, then the pair 〈 M G, M F 〉 does not have Fubini property.

TL;DR: In this paper, it was shown that Mathias forcing associated with the complement of an analytic ideal always adds a dominating real, and that such forcing with summable ideals is mutually bi-embeddable.

TL;DR: It is proved that for an analytic ideal I, either the ideal is Rudin-Keisler below I, or I is very simply induced by a lower semicontinuous submeasure, and it is shown that the class of ideals induced in this manner by lsc submeasures coincides with Polishable ideals as well as analytic P-ideals.

TL;DR: In this article, the reciprocal matrix M-1 can be computed rapidly and simply in the two cases where M is a moment matrix or an alternant matrix, and the coefficients in the polynomials are determined by the equation where c is the column of coefficients, h is a column of known constants, and M is the matrix which depends on the method of representation adopted.

TL;DR: In this paper, the authors studied combinatorial properties of the partial order (Dense(Q); ) and introduced cardinal invariants pQ; tQ; hQ; sQ; rQ; iQ describing properties of dense(Q), and compared them with their analogues in the well studied Boolean algebra P(!)=n.