I am going to teach a course in set theory for software engineering students.I am going to talk in this course about: ordinal numbers, partial orders, well ordering, generic filters and maybe some cardinal invariants (such as $\mathfrak b$, $\mathfrak d$). I might also give a gentel introduction to forcing theory. I was asked by the head of the department, to add to this course some application of this theory to software engineering.Since my main area is math and not computer science, I don't have an idea for such an application.Any ideas for such an application? If there is I would be greatfull if you could give me a detailed source.Thank you!
Application of set theory subjects as ordinals, forcing, generic filters in software engineering
discrete mathematics;type theory;sets;software engineering;applied theory
The areas of set theory you refer to are generally rather abstract and don't seem to have a lot of applications. Also, the concept of application is different in math than in CS. Anyway, though applied CS is so vast now that even very abstract concepts can find applications somewhere. Here is one possible link. This paper Tree Automata Make Ordinal Theory Easy (Cachat) shows that tree automata can be used as representing ordinal sets with infinite trees. Then, once connected to automata, there are many practical applications of automata. (There are possibly other connections with Buchi automata.) We give a new simple proof of the decidability of the First  Order Theory of ($\omega^{\omega^i}, +)$ and the Monadic Second Order Theory of  $(\omega^i, <),$ improving the complexity in both cases. Our algorithm is based  on tree automata and a new representation of (sets of) ordinals by (infinite) trees.Another idea, this blog quotes a reference that ordinal theory is used in High Frequency Trading (HFT) algorithms but there seem to be few other independent references to this on the internet. This could be explained in that HFT field is very secretive with its technology, or possibly that it's erroneous, but the claim has been repeated widely.