Mathematical logic, set theory, lattices and universal algebra form an interconnected framework that underpins much of modern mathematics. At its heart, mathematical logic provides rigorous formal ...

Transfinite set theory encompasses the rigorous study of infinite hierarchies, particularly those structured by ordinals and cardinals. This field has been instrumental in deepening our comprehension ...

We try to answer the question which is the "right" foundation of mathematics, second order logic or set theory. Since the former is usually thought of as a formal language and the latter as a first ...

According to Cantor (Mathematische Annalen 21:545—586, 1883; Cantor's letter to Dedekind, 1899) a set is any multitude which can be thought of as one ("jedes Viele, welches sich als Eines denken läßt" ...

Unlike his much more famous colleague Albert Einstein, John von Neumann is not a household name these days, but his discoveries shape the possibilities of life for every creature on this planet. As a ...