Logic Seminar in AY 2025/2026 at NUS

• Wednesday 13/08/2025, 17:00 hrs, Week 1, Department of Mathematics, Room S17#05-11.
  Kenny Gill. Computational properties of indivisible structures.
  A countable structure S is indivisible if it satisfies a pigeonhole principle: for any bounded coloring of any presentation of S, there is a monochromatic induced substructure isomorphic to S. This naturally gives rise to an instance-solution problem Ind(S) which outputs such a substructure given a presentation and coloring. We seek to understand both (1) the computational difficulty of solving Ind(S) for various specific S; and (2) how properties of S can translate to properties of Ind(S) and vice versa. This talk will survey what is known about both (1) and (2), highlighting some of the many open problems in the area. In particular, we propose several notions of uniform embeddability of one structure in another which allow one to obtain desirable properties of Ind(S) for large classes of S.
  This is in part ongoing joint work with Damir Dzhafarov and Reed Solomon.
  
  
• Wednesday 20/08/2025, 17:00 hrs, Week 2, Department of Mathematics, Room S17#05-11.
  Tran Chieu Minh. Large implies Henselianity.
  In the classic paper ``Henselianity implies large’’, Pop showed that a field is large if it is elementarily equivalent to the fraction field of a proper Henselian local domain. We show that it can, in fact, be improved to an ``if and only if’’ statement.
  We will explain how this result arises from the effort to introduce canonical topologies over a field, namely, a result comparing the etale-open topology with a newly introduced finite-closed topology.
  This is joint work with Will Johnson, Erik Walsberg, and Jinhe Ye.
  
  
• Wednesday 27/08/2025, 17:00 hrs, Week 3, Department of Mathematics, Room S17#05-11.
  Yang Yue. Halpern-Läuchli Theorem and Mathematical Induction.
  I will talk about Halpern-Läuchli Theorem (HL) and its proof(s). This is an ongoing project with Chong Chitat and Li Wei, aiming to find the proof-theoretic strength of HL. I will sketch a proof that under Σ₃-induction, there is a computable solution for HL.
  
  
• Wednesday 03/09/2025, 17:00 hrs, Week 4, Department of Mathematics, Room S17#05-11.
  No talk.
  
  
• Wednesday 10/09/2025, 17:00 hrs, Week 5, Department of Mathematics, Room S17#05-11.
  Frank Stephan. Minimal one-one degrees in recursively enumerable many-one degrees.
  Dëgtev constructed in 1976 recursively enumerable many-one degrees with the following properties: no least one-one degrees inside the many-one degree; one least but no minimal one-one degree inside the many-one degree; for each natural number k one least and above the least k minimal one-one degrees inside the given many-one degree (which, of course, depends on k). He did not provide a recursively enumerable many-one degree with infinitely many minimal one-one degrees and Odifreddi put it in 1981 as an open question into his survey paper. According to Batyrshin, the question was in 2021 still open. This talk will now provide the construction of such a many-one degree with infinitely many minimal one-one degrees. Such a degree has a least one-one degree below them.
  This is joint work with Sanjay Jain, Linus Richter, Samuel Alfaro Tanuwijaya and Xiaoyan Zhang; a write-up is under preparation.
  
  
• Wednesday 17/09/2025, 16:45 hrs, Week 6, Department of Mathematics, Room S17#05-11.
  Andrea Volpi. Effectiveness and strong graph indivisibility.
  A relational structure is strongly indivisible if for every partition M = X ⊔ Y, the induced substructure on X or Y is isomorphic to M. Cameron (1997) showed that a graph is strongly indivisible if and only if it is the complete graph, the completely disconnected graph or the random graph. We analyze the strength of Cameron's theorem using tools from computability theory and reverse mathematics. We show that Cameron's theorem is is effective up to computable presentation and give a partial result towards showing that the full theorem holds in the ω-model REC. We also establish that Cameron's original proof makes essential use of the stronger induction scheme IΣ₂.
  This is joint work with Damir Dzhafarov and Reed Solomon.
  
  
• Wednesday 01/10/2025, 17:00 hrs, Week 7, Department of Mathematics, Room S17#05-11.
  
  
  
• Wednesday 08/10/2025, 17:00 hrs, Week 8, Department of Mathematics, Room S17#05-11.
  
  
  
• Wednesday 15/10/2025, 17:00 hrs, Week 9, Department of Mathematics, Room S17#05-11.
  
  
  
• Wednesday 22/10/2025, 17:00 hrs, Week 10, Department of Mathematics, Room S17#05-11.
  
  
  
• Wednesday 29/10/2025, 16:45 hrs, Week 11, Department of Mathematics, Room S17#05-11.
  
  
  
• Wednesday 05/11/2025, 17:00 hrs, Week 12, Department of Mathematics, Room S17#05-11.
  
  
  
• Wednesday 12/11/2025, 17:00 hrs, Week 13, Department of Mathematics, Room S17#05-11.