I received my Bachelor of Software Engineering in 2009 from Northeast Normal University, and Master of Logic in 20011 from University of Amsterdam. In 2011 I started working as a Ph.D. candidate at the Institute for Logic, Language and Computation (ILLC), University of Amsterdam, specializing in mathematical logic and focussing on finding meaningful structures on classes of infinitary mathematical objects using computability tools. I worked on research projects that involve computability theory, algorithmic randomness, computable structures, descriptive set theory, and infinite games. In 2014 I decided to move out of academia and start a career in business and technology. I am now doing research as a hobby.
Projects and papers
Games and Set Theory
Under the supervision of Professor Benedikt Löwe, I wrote my thesis Degrees of Non-Determinacy and Game Logics on Cardinals under The Axiom of Determinacy. The abstract is here. I put the most important results of my master thesis in the unpublished paper Degrees of Non-determinacy of Infinite Games without The Axiom of Choice.
I solved a small interesting problem together with George Barmpalias. We put the result in the unpublished paper Every Set of Non-random Strings Is rK-complete.
Effectively Open Games And Linear Logic
This project was motivated by a inspiring discussion with Professor Benedikt Löwe and Professor Andreas R. Blass in 2011. It is an interesting combination of computability theory, game semantics, and linear logic. I am working on the draft paper A Degree Structure on Effective Open Or Closed Games And Game Semantics of Linear Logic.
Uniform Effectiveness of Ordinal Functions
I started this project with Professor Joel David Hamkins when we were both vising University of Cambridge. We introduced the notion of uniformly effectiveness of operations on well orderings, which matches the intuitive idea that an algorithm performing the operation should work on any representations of the well orderings.
The draft paper On Effectiveness of Operations on Countable Ordinals contains many interesting results on well orderings, Turing degrees, Medvedev degrees, and uniform computability. In the paper we developed tools for showing uniform effectiveness/non-effectiveness of operations on ordinals. We gave new and more elementary proofs to some well-known results, and proved new results that give us insight for understanding well orderings and computability. We believe that this project will see more interesting results.
Structures that permit minimal Turing degrees
The problem is to characterize those countable structures, e.g., the countable dense linear ordering without endpoints, which have representations (in the Cantor space) having minimal Turing degrees. Note that for each signature (of a structure) we can fix a Gödel's arithmeticalization to talk about representations in the Cantor space of structures having that signature. I started this project in 2013 when I was visiting Professor Theodore A. Slaman and Professor Antonio Montalbán at UC Berkeley. This project is at a beginning stage and the first attempt to solve this question can be found in this small paper Structures That Have Minimal Degrees.
"Structures that permit minimal Turing degrees", Logic Tea, Institute for Logic, Language and Computation, Amsterdam, 13 May 2014.
"Degrees of non-determinacy of infinite games without the axiomof choice", Logic Colloquium 2013, Évora, Portugal, 22-27 July 2013.
"Computable functionals on the countable ordinals", Colloquium Logicum 2012, Paderborn, Germany, 13-15 September 2012.
"Computable functionals on the countable ordinals", Logic Tea, Institute for Logic, Language and Computation, Amsterdam, 11 September 2012.
"Degrees of non-determinacy of computable games and linear logic", Institute of Software, Chinese Academy of Sciences (ISCAS), Beijing, China, 5 January 2012.
"Blass's game semantics for linear logic without the axioms of choice", Modern Set Theory: Foundations & Applications, Ljubljana, Slovenia, 1-5 August 2011.
TA for Axiomatic Set Theory (Benedikt Löwe)
TA for Basic Logic (Frank Veltman)
TA for Model Theory (Yde Venema)
TA for Axiomatic Set Theory (Alexandru Baltag)
TA for Capita Selecta: Set Theory (Benedikt Löwe)
Set Theory Lunch Seminar, Institute for Logic, Language and Computation, Amsterdam, 2012-2013
Amsterdam Workshop in Set Theory, Amsterdam, 10-11 February, 2012
The old homepage http://staff.science.uva.nl/~zhenhao/ stopped working due to sever shutdown. The homepage address is to be updated on my info page http://www.illc.uva.nl/People/show_person.php?Person_id=Li+Z.