**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)