泛代数中提升问题引起的无限组合问题
Infinite combinatorial issues raised by lifting problems in universal algebra
摘要：
代数簇A和B之间的临界点定义为A中的一个成员的紧同余的半格的最小基数，如果它存在的话，B中没有成员。对临界点的研究产生了一系列的问题，通常涉及到图或对象的提升问题。这些，反过来，涉及的问题，属于无限组合学。我们调查的一些组合的问题和结果，从而遇到的。相应的问题是围绕k-阶梯的概念（用于证明临界点是大的），大自由集定理和经典符号（k，r，l）{ \to }m（用于证明临界点是小的）。在中间，我们找到偏序集的l-提升子和关系（k，< l）{ \to }P，对于无限基数k和l以及偏序集P。
英文摘要：
The critical point between varieties A and B of algebras is defined as the least cardinality of the semilattice of compact congruences of a member of A but of no member of B, if it exists. The study of critical points gives rise to a whole array of problems, often involving lifting problems of either diagrams or objects, with respect to functors. These, in turn, involve problems that belong to infinite combinatorics. We survey some of the combinatorial problems and results thus encountered. The corresponding problematic is articulated around the notion of a k-ladder (for proving that a critical point is large), large free set theorems and the classical notation (k,r,l){\to}m (for proving that a critical point is small). In the middle, we find l-lifters of posets and the relation (k, < l){\to}P, for infinite cardinals k and l and a poset P.
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