Logan Heath

I am a fifth year Ph.D. student at the University of Wisconsin–Madison studying mathematical logic with Uri Andrews. My interests are in the area of computable model theory and degree spectra of theories. Questions I am interested in have the form "Is there a theory T with model theoretic property X such that no theory with the same spectrum has model theoretic property Y?" For example, Andrews and Miller (2015) constructed a theory having the PA degrees as its spectrum and showed that no theory with the same spectrum is atomic. A careful look at their work shows the theory to be superstable thereby giving an example of a superstable theory whose spectrum is not the spectrum of any atomic theory. There are few other results of this sort and I am currently focused on finding theory/spectra pairs that sharply divide between the various levels of stability. For instance, I would like a spectrum that divides between superstable and ω-stable without necessarily avoiding some class of theories strictly containing the ω-stable ones (e.g. the small theories).

e-mail: laheath (at) wisc (dot) edu
Office: 516 Van Vleck Hall