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 containing the ω-stable ones (e.g. the small theories).

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