The purpose of this note is to discuss the local lifting property in terms of an equivalent approximation-type property, CP-stability, which was formulated by the author and Isaac Goldbring for the purposes of studying the continuous model theory of C∗-algebras and operator systems.

We give new formulations of the property of soundness and completeness of a resolution system and of the lifting lemma, and we discuss their relationship. The discussion points out why certain resolution systems are not complete, and that there is a simple method for showing that a resolution system is \absolutely incomplete" { that there is no notion of program completion and no logic which co...

Combinatorial commutation properties for reordering a sequence consisting of two kinds of steps, and for separating the well-foundedness of their combination into well-foundedness of each, are investigated. A weak commutation property, called “jumping”, along with a weakened version of the lifting property, called “escaping” and requiring only an eventual lifting, are used for proving wellfound...

March 7, 2000 Abstract. A Banach space X is said to have the separable lifting property if for every subspace Y of X containing X and such that Y/X is separable there exists a bounded linear lifting from Y/X to Y . We show that if a sequence of Banach spaces E1, E2, . . . has the joint uniform approximation property and En is c-complemented in E∗∗ n for every n (with c fixed), then P n En 0 has...

For logical thinking learners, it is important to learn problem solving formally and intuitively. Homotopy which is modern mathematics combines algebra and geometry together. Homotopy gives the most abstract level of explanation or the most basic invariant which is the most required characteristics for logical thinking. The homotopy lifting property gives good explanation of inductive reasoning...

Lifting is a procedure for deriving strong valid inequalities for a closed set from inequalities that are valid for its lower dimensional restrictions. It is arguably one of the most effective ways of strengthening linear programming relaxations of 0–1 programming problems. Wolsey (1977) and Gu et al. (2000) show that superadditive lifting functions lead to sequence independent lifting of valid...