Hi! I'm an NSF postdoc at UW - Madison (Fall 2016 - Spring 2019), working primarily with Uri Andrews, Steffen Lempp, Joe Miller, and Mariya Soskova.

My email is schweber@wisc.edu.

Here is my CV.

I'm active on mathoverflow and math.stackexchange, and often work at Canada/USA Mathcamp in the summer.


In Spring 2018 I taught Math 222 (calculus and analytic geometry 2); in Spring 2019 I will be teaching Math 551 (point-set topology).

Research interests

My research is in mathematical logic. Mostly I look at computability theory, reverse mathematics, set theory, and their interactions, but I'm also interested in proof theory and abstract model theory. I'm especially interested in generalized computability theory in its various flavors: descriptive set theory, uncountable computable structure theory, higher reverse mathematics, and notions of set recursion. (Since generalized computability theory is a messy subject to navigate, here is a amateur annotated bibliography.)


"Logical complexity of Banach-Mazur games." In preparation.

"The complexity of expansions of Cantor and Baire space." With Uri Andrews, Joe Miller, and Mariya Soskova. In preparation.

"Effective localization number: building $k$-surviving degrees." With Ivan Valverde. In preparation.

"Theories satisfying 'arithmetic-is-recursive.'" With Uri Andrews, Matthew Harrison-Trainor, and Joe Miller. In preparation.

"Natural examples of many-one incompleteness in the $\kappa$-Turing degrees." With Reese Johnston. In preparation.

"The axiom of choice in higher reverse mathematics." Submitted.

"Set theory and strong reducibilities." Submitted.

"Medvedev reducibility and $\alpha$-recursion theory." Submitted.

"Limit computability and ultrafilters." With Uri Andrews, Mingzhong Cai, and David Diamondstone. Submitted.

"Computing strength of structures related to the field of real numbers." With Greg Igusa and Julia Knight. Journal of Symbolic Logic, 82(1), pp. 137-150, 2017.

"Computable structures in generic extensions." With Antonio Montalban and Julia Knight. Journal of Symbolic Logic, 81(3), pp. 814-832, 2016.

"Transfinite recursion in higher reverse mathematics." Journal of Symbolic Logic, 80(3), pp.940-969, 2015.

"Computably enumerable partial orders." With Peter Cholak, Damir Dzhafarov, and Richard Shore. Computability, 1(2), pp. 99-107, 2012.

Subpages (1): Math 551 course site
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