Consider the following decision problem, over the equality symmetry.
Input: an orbit-finite system of linear equations over
Decide: does have a solution (not necessarily finitely-supported)?
Inspired by Eryk’s beautiful solution of this problem, we present another solution, using an amazing theorem from topological dynamics.
It can happen that two equivariant sets with atoms are related by a finitely supported bijection, but not by an equivariant bijection.
There are several decision problems for certain computation models with atoms that are decidable when atoms admit certain well quasi order (WQO), and undecidable otherwise. We recall the problems and formulate few questions related to WQOs.
Čech cohomology is a way of defining cohomology groups (a topological invariant with algebraic structure) on a topological space. We give a rough description of the construction, in a very special case of a torus, and relate it to the construction of the nonstandard alphabets. Continue reading
A set is orbit finite if and only if the number of its elements supported by atoms grows polynomially with .
Again, a question closely related to a characterization of standard atoms (not to be confused with standard alphabets:). The question is a refinement of a question posted in Automorphisms vs color-preserving automorphisms in Fraisse classes, which has been answered negatively (see the recent post The colored open question closed).