1968/01/01 by S. Tennenbaum · 1 citation
Mathematics · Chemistry · #Holomorphic and Operator Theory #Analytic and geometric function theory #Algebraic and Geometric Analysis #Chemistry #Computational biology #Computer science #Biology
paper · doi:10.1073/pnas.59.1.60
openalex publication_date 1968/01/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/06/11
In this note we apply the method of P. J. Cohen" 2 to the following problem of Souslin3: Let S be a linearly ordered continuous set without first and last elements in which every family of disjoint intervals is countable.Is S isomorphic to the real line?We obtain models of the contemporary axioms for set theory in which the answer is negative.Moreover, in one of these the continuum hy- pothesis holds, and in others it fails.In a later paper,4 written with R. Solovay, Cohen's method is extended to define models in which the answer is affirmative.Thus the current axioms do not suffice to settle Souslin's problem.For convenience, the following version of the problem will be considered: Let T be a tree' such that every chain and antichain! in T has cardinality less than %4.but the field of T has cardinality 4a.Call such a T an %4.-Souslin tree.