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 ...

Paul Cohen's method of forcing, together with Saul Kripke's related semantics for modal and intuitionistic logic, has had profound effects on a number of branches of mathematical logic, from set ...

Set theory is a mathematical abstract concerned with the grouping of sets of numbers that have commonality. For example, all even numbers make up a set, and all odd numbers comprise a set. All numbers ...

The equal sign is the bedrock of mathematics. It seems to make an entirely fundamental and uncontroversial statement: These things are exactly the same. But there is ...

A pair of researchers has shown that trying to classify groups of numbers called “torsion-free abelian groups” is as hard as it can possibly be. The Quanta Newsletter ...

Emily Riehl thinks hard about objects that don't exist in the material world yet mysteriously seem to underlie many things that do. These objects have no concrete existence of their own, but they do ...