Well ordered subsets of linearly ordered sets
The authors investigate the strength of Davis' theorem LFC in the hierarchy of weak choice principles. LFC is the assertion that linear orders with the fixed point property for monotone mappings are complete. LFC is in strength between CF and DS. Here CF is the axiom that every linearly ordered set has a cofinal well-ordered subset. DS is the statement that a linear ordering without an infinite descending subsequence is a well-ordering. The main result of the paper is the construction of Fraenkel-Mostowski permutation models which show that DS does not imply LFC and LFC does not imply CF.
scientific article; zbMATH DE number 769233