From mereology to boolean algebra
the role of regular open sets in alfred Tarski's work
pp. 259-277
in: Kevin Mulligan, Tomasz Placek (eds), The history and philosophy of Polish logic, Berlin, Springer, 2014Abstract
Can the content of a whole paper be explained by a single footnotę In 1956 Alfred Tarski made an effort in this direction in his chapter "On the Foundations of Boolean Algebra' (Tarski, 1956c). This chapter had originally appeared as the paper "Zur Grundlegung der Boole'schen Algebra, I' (Tarski, 1935), the sequel of which had never been published. This sequel should have contained, among other things, the atomless system of Boolean algebra, as Tarski points out (Tarski, 1956c, p. 341, fn. 2). In that same footnote Tarski also gives a model for atomless Boolean algebra, consisting of the family of so-called regular open sets of a Euclidean space and the relation of set-inclusion. He then refers back to another chapter in Tarski (1956b): Foundations of the Geometry of Solids (Tarski, 1956a). This reference and the model of atomless Boolean algebra appear only in the 1956 edition (Tarski, 1956c); they are absent in Tarski (1935).
