The Adams Thesis holds for a conditional and a probability assignment if and only if whenever . The restriction ensures that is well defined by the classical formula . Drawing on deep results of Maharam on measure algebras, it is shown that, notwithstanding well-known triviality results (Lewis, etc.), any probability space can be extended to a probability space with a new conditional satisfying the Adams Thesis and satisfying a number of axioms for conditionals. This puts significant limits on how far triviality results can go.
"Conditionals and Conditional Probabilities without Triviality." Notre Dame J. Formal Logic 60 (3) 551 - 558, August 2019. https://doi.org/10.1215/00294527-2019-0019