Mathias and Silver forcing parametrized by density

Mathias 力迫与 Silver 力迫的恰当与非恰当变体

Proper and Improper Variants of Mathias and Silver Forcing

该研究解答了 Mathias 与 Silver 力迫密度变体的恰当性及添加支配实数、Cohen 实数等问题，并将证明推广到满足条件的下半连续子测度参数化 Mathias 力迫。

Submaximal spaces and cardinal invariants

We give a combinatorial characterization of countable submaximal subspaces of $2^κ$. Using a parametrized version of Mathias forcing, we prove that there exists a countable submaximal subspace of $2^{ω_1}$ whilst $\mathfrak{c}=ω_2$. Combining this with previous results, we construct a disjointly tight countable irresolvable space of weight $<\mathfrak{c}$, answering a question of Bella and Hrušák.