This undergraduate/graduate course emphasized topics close to dynamic epistemic logic and
also used a new didactic approach to the completeness and decidability results for the basic modal systems.
I am re-working the notes from this course into a textbook.
If you are a teacher or student of modal logic and would like to see the current version, please let me know.
A course for non-majors on mathematical topics motivated by language, especially the basics
of syntax and semantics.
M682: Model Theory
A computer program that trades places with all possible inputs
Believe it or not,
the image above really is a computer program. It is connected to this semester's Recursion Theory course.
In 1938, my academic grandfather Stephen Kleene published a paper containing a result called the Second Recursion Theorem.
This result has many consequences in many areas of mathematical logic.
As just one of its minor consequences, it
the famous result
that in any programming language, there is a computer program self such that running self outputs self itself. The program below, trade, has an even stronger property.
To state it, we must consider programs running on other programs in the same language.
When trade is run on any program p, the output would be the same as the result of running
this same program p on trade. Although the existence of trade follows from the Second Recursion Theorem, it seems that nobody exhibited a trade program in full glory. Above, you'll find a portion of such a trade program, written in a language called 1#. Programs in 1# are not readable, but the language can be explained in a paragraph that is shorter than this one. The trade program has 13,035 instructions.
Some of the parts in color are independently interesting: the red part at the bottom is a universal program.