David Gonzalez

Society of Science Postdoctoral Fellow

Education

PhD University of California, Berkeley - 2025

B.S Stanford University, Palo Alto - 2019

Research Group

Logic

Bio

Research Interests

My research lies in mathematical logic, with a primary focus on computability theory. My work explores the rich intersections of this field with countable model theory, countable combinatorics, and descriptive set theory, analyzing problems from both structural and topological viewpoints. I am also actively engaged in reverse mathematics, a program that seeks to determine the minimal axioms needed to prove specific theorems, thereby understanding the combinatorial core of mathematical proofs. To get a more specific understanding of my work, feel free to start with the papers listed below or visit my personal webpage for more information.

Selected Publications

• D. Gonzalez and A. Montalbán, The omega Vaught’s conjecture. Trans. Amer. Math. Soc., 376 (2023), no. 8, 5989–6008.
• D. Gonzalez, M. Harrison-Trainor, M. Ho, Semi-periodic Functions and the Scott Analysis of Linear Orderings. Bull. Lond. Math. Soc., 57 (2025), no. 4, 1118-1139

• D. Gonzalez and M. Harrison-Trainor, Scott Spectral Gaps are Bounded for Linear Orderings. Submitted for publication.

• R. Chen, D. Gonzalez and M. Harrison-Trainor, Optimal Syntactic Definitions for Back-and-Forth Types. Submitted for publication.

• D. Cenzer, W. Calvert, D. Gonzalez, V. Harizanov, and K. Ng, Homogeneous Linear Orderings: Index Sets, Approximations and Categoricity