I am currently a mathematics undergraduate with every intention to enter a top mathematics PhD program in the future. I understand that having research experiences as an undergraduate is one of the key aspects of making your applications sufficiently strong to be considered, and as such, I have participated/am participating in a couple of undergraduate research projects.
Here is the problem: While I have been interested mostly in number theory/analysis in my earlier days as an undergraduate, only recently have I realised that I'm most interested in set theory. I have completed one undergraduate research on number theory (not publishable but was published on a small, local mathematical journal), and am currently participating in a project related to PDE, which is very heavy on functional/nonlinear analysis (this project is expected to lead to a publishable article). As one can tell, these two projects have completely no relation to set theory. I also have one final project to undertake, which is my final year project, and I intend to research on set theory on this project.
Should I ultimately decide to apply for PhD under the set theory/logic department in the future, how much would my past research experiences in other fields help in my application?
I appreciate any advice provided.