World Logic Day Workshop 2023
January 16, 2023
Research Fellow
Sapienza University of Rome, Italy.
Title of the talk: Settling algebraic questions with logic.
Abstract: In this talk, we revisit word problems through the lens of the theory of equivalence relations, which has grown immensely in recent decades. To do so, we employ computable reducibility, a natural effectivization of Borel reducibility. This is joint work with Valentino Delle Rose and Andrea Sorbi.
Time: 17:30-18:15 (Astana time, UTC+6);
Professor at the Departments of Mathematics and Computer Science of the National University of Singapore.
Title of the talk: On Trees without Hyperimmune Branches.
Abstract: In the year 2013, Keng Meng Ng, Frank Stephan, Yue Yang and Liang Yu published the paper "Computational Aspects of the Hyperimmune-free Degrees" and one of the results was given without a full proof. The current talk gives the full proof of this result. In particular, the talk provides the full details of the construction of an co-r.e. infinite binary tree with uncountablly many branches which are all hyperimmune-free, Schnorr-trivial, jump traceable, generalised low and of minimal Turing degree. Hyperimmune-free means that every function Turing reducible to it is majorised by a recursive function. Jump traceable means that for every e one can compute an explicit bound on the number of elements which some further set also depending on e enumerates and that finite set contains the Jump value at e. Generalised low means that the jump of A is recursive in the join of A and K. A minimal Turing degree is a nonrecursive Turing degree below which is only the recursive one. Schnorr trivial means that for every f truth-table reducible to the set there is a recursive function which lists out for each input x a set of x+1 many values with one of them being f(x).
Time: 18:15-19:00 (Astana time, UTC+6);
Professor
Kazakh-British Technical University, Kazakhstan.
Title of the talk: Some results on variants of o-minimality.
Abstract: Here we present recent results obtained at studying variants of o-minimality: weak o-minimality and weak circular minimality. In particular, questions concerning almost omega-categoricity, the number of countable models, and algebras of binary isolating formulas are considered.
Time: 19:00-19:45 (Astana time, UTC+6);