- Research
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.
- Publications
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
A Short Introduction to Admissible Recursion Theory
R. Alvir. “Zero Divisior Graphs of Quotient Rings.” Preprint. (2015)