More on the lifting problem with the full ideal

New Results on Congruence Boolean Lifting Property

The Lifting Idempotent Property ($LIP$) of ideals in commutative rings inspired the study of Boolean lifting properties in the context of other concrete algebraic structures ($MV$-algebras, commutative l-groups, $BL$-algebras, bounded distributive lattices, residuated lattices,etc.), as well as for some types of universal algebras (C. Muresan and the author defined and studied the Congruence Boolean Lifting Property ($CBLP$) for congruence modular algebras). A lifting ideal of a ring $R$ is an ideal of $R$ fulfilling $LIP$. In a recent paper, Tarizadeh and Sharma obtained new results on liftin…

Biba的技巧及其应用

Biba's trick, with applications

本文通过改进OCA提升定理并简化证明，扩展了可数确定理想的提升结果，进一步支持力迫公理在商结构刚性中的框架作用。

Strongest transformations

We continue our study of maps transforming high-dimensional complicated objects into squares of stationary sets. Previously, we proved that many such transformations exist in ZFC, and here we address the consistency of the strongest conceivable transformations. Along the way, we obtain new results on Shelah's coloring principle $Pr_1$. For $κ$ inaccessible, we prove the consistency of $Pr_1(κ,κ,κ,κ)$. For successors of regulars, we obtain a full lifting of Galvin's 1980 theorem. In contrast, the full lifting of Galvin's theorem to successors of singulars is shown to be inconsistent.