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 ...

We recently wrote about how infinitely large sets are not all the same size as each other, but we were a bit vague about what we meant by a set. The people who invented set theory also started out ...

To introduce the students to the general theory of sets, as a foundational and as an axiomatic theory. The aim is to make the course of general interest to students who are not planning to specialize ...

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 ...

When a legendary mathematician found a mistake in his own work, he embarked on a computer-aided quest to eliminate human error. To succeed, he has to rewrite the ...