The Dual of a Refinement Algebra
Rae Michael Shortt, K. P. S. Bhaskara Rao · 2020
The notion of cardinal algebra provides a common generalization for a number of important mathematical structures: non—negative real numbers under addition, cr-distributive a— lattices under the operation of supremum, sets of non—negative measurable functions and countably additive measures on a measurable space under point—wise summation, and sets of Borel—isomorphism types under topological (or Borel) sum. As developed by Tarski and set forth in his masterful book [ 11 ], the distinctive feature of this theory is its essential use of an infinitary operation corresponding in most examples to summation or countable supremum. A number of applications have been assayed in the areas of algebra, descriptive set theory and measure theory, although the theory has in recent years settled into a modest quiescence. A sample set of references might include [ 1 ] - [ 8 ] and of course [ 11 ].