A convergence on Boolean algebras generalizing the convergence on the Aleksandrov cube
英文摘要：
We compare the forcing related properties of a complete Boolean algebra B with the properties of the convergences $λ_s$ (the algebraic convergence) and $λ_{ls}$ on B generalizing the convergence on the Cantor and Aleksandrov cube respectively. In particular we show that $λ_{ls}$ is a topological convergence iff forcing by B does not produce new reals and that $λ_{ls}$ is weakly topological if B satisfies condition $(\hbar)$ (implied by the ${\mathfrak t}$-cc). On the other hand, if $λ_{ls}$ is a weakly topological convergence, then B is a $2^{\mathfrak h}$-cc algebra or in some generic extension the distributivity number of the ground model is greater than or equal to the tower number of the extension. So, the statement "The convergence $λ_{ls}$ on the collapsing algebra $B=\ro ((ω_2)^{<ω})$ is weakly topological" is independent of ZFC.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
