I recently got in contact with Prof. Balder (in Logic and Probability (Lecture)), who has worked in Finite Model Theory, and I think this could be a particularly interesting area for me to explore further in mathematical logic. This might provide a potential answer to the question I posed in Is it the Begin of a Motivational Decline: one of the main concerns I had there was finding a proper methodology or criteria to identify a field captivating enough to dedicate most of the upcoming years to. Some of these criteria will likely depend on the PhD Applications Results, while others are independent of them and might be relevant if I get into one of the PhD Applications in the US, as they impose no constraints on a specific programme.
Regarding Finite Model Theory, I see several aspects that I find particularly attractive, and I will try to list them here while keeping in mind that I currently have no precise knowledge of what the field entails.
First, I was deeply interested in Model Theory (Lecture) when I took the course at the University of Constance and will have a similar lecture again at the ILLC Amsterdam, namely Model Theory bis (Lecture). I have also recently applied some notions from it in Ontic Structuralism of Concepts. This confirms that I am very much engaged in model theory and consider it one of the most intriguing fields in mathematical logic.
Secondly, one major advantage of Finite Model Theory is its strong applicability in Computer Science, making it a particularly versatile area within mathematical logic. Keeping career paths open in directions similar to Balder’s (see LinkedIn) could provide some diversity in my future studies, allowing for a mix between academia and industry.
Lastly, Finite Model Theory—likely as much as Model Theory—may have interesting developments in neighbouring fields that I am highly interested in, ranging from Philosophy and Model Theory (2018) to its connections with Translation Theory, other areas of mathematical logic (but also Algebra, Graph Theory, Modal Logic), and its applications in computer science. It might therefore play a central role in several disciplines I am drawn to.