A Logical Interpretation of Some Bits of Topology

Edit: These ideas are also discussed here and here (thanks to Qiaochu Yuan: I found out about those links by him linking back to this post). Although topology is usually motivated as a study of spatial structures, you can interpret topological spaces as being a particular type of logic, and give a purely logical, non-spatial […]

Topology and First-Order Modal Logic

The normal square root function can be considered to be multi-valued. Let’s momentarily accept the heresy of saying that the square root of a negative number is , so that our function will be total. How can we represent the situation of this branching “function” topologically?

Two Interesting Observations about Voting I Hadn’t Seen Until Recently

By “voting”, I mean the following general problem:  Suppose there are candidates and voters.  Each voter produces a total ordering of all candidates.  A voting procedure is a function which takes as input all orderings, and produces an output ranking of all candidates.  Arrow’s impossibility theorem states that there is really no satisfactory voting procedure […]

A Suite of Cool Logic Programs

You may have heard about the Tarski-Seidenberg theorem, which says that the first-order theory of the reals is decidable, that the first-order theory of the complex numbers is similarly decidable, or that the first order theory of the integers without multiplication is decidable. In the course of John Harrison‘s logic textbook Handbook of Practical Logic […]