My interests in both mathematics and philosophy deal with circumventing Gödel’s incompleteness theorems. In mathematical logic, I study computable structure theory. I ask when it is possible to describe a structure up to isomorphism among models of the same cardinality in infinitary first-order languages, and compute exactly how difficult it is to give such a description when possible. My research also intersects with general recursion theory and set theory. In philosophy, I am interested in Gödel as a historical figure and fulfilling what I call “Gödel’s Program:” defending the truth of the axioms of ZFC and the decidability of CH in some nonarbitrary formal system.
My hair changes a lot, so you may not recognize me from time to time.
R. Alvir, D. Rossegger. “Scott Ranks of Scattered Linear Orders.” In preparation.
R. Alvir, J. Knight, and C. McCoy. “Complexity of Scott Sentences.” Submitted. (2017)
- Preprints and Notes