Call a family F of subsets of a set E inductive if âˆ… âˆˆ F and F is closed under unions with disjoint singletons, that is, if âˆ€XâˆˆF âˆ€xâˆˆEâ€“X(X âˆª {x} âˆˆ F]. A Frege structure is a pair (E, Î½) with Î½ a mapâ€¦ (More)

By Frege's Theorem is meant the result, implicit in Frege's Grundlagen, that, for any set E, if there exists a map Î½ from the power set of E to E satisfying the condition âˆ€XY[ Î½(X) = Î½(Y) â‡” X â‰ˆ Y] ,â€¦ (More)

Hermann Weyl (1885 â€“ 1955) was one of the greatest and most versatile mathematicians of the 20th century. His work had a vast range, encompassing analysis, algebra, number theory, topology,â€¦ (More)

THE CLOSE CONNECTION BETWEEN mathematics and philosophy has long been recognized by practitioners of both disciplines. The apparent timelessness of mathematical truth, the exactness and objectiveâ€¦ (More)

The principle of set theory known as the Axiom of Choice (AC) has been hailed as â€œprobably the most interesting and, in spite of its late appearance, the most discussed axiom of mathematics, secondâ€¦ (More)