Suppose that the vertices of Z are assigned random colors via a finitary factor of independent identically distributed (iid) vertex-labels. That is, the color of vertex v is determined by a rule that examines the labels within a finite (but random and perhaps unbounded) distance R of v, and the same rule applies at all vertices. We investigate the tail behavior of R if the coloring is required ...

A ‘resolution’ of the interior singularity of the spherically symmetric Schwarzschild solution of the Einstein equations for the gravitational field of a point-particle is carried out entirely and solely by finitistic and algebraic means. To this end, the background differential spacetime manifold and, in extenso, Calculus-free purely algebraic (:sheaf-theoretic) conceptual and technical machin...

We develop Morita theory for finitary additive 2-representations of finitary 2-categories. As an application we describe Morita equivalence classes for 2-categories of projective functors associated to finite dimensional algebras and for 2-categories of Soergel bimodules.

We study two-player zero-sum games over infinite-state graphs with boundedness conditions. Our first contribution is about the strategy complexity, i.e the memory required for winning strategies: we prove that over general infinite-state graphs, memoryless strategies are sufficient for finitary Büchi games, and finite-memory suffices for finitary parity games. We then study pushdown boundedness...

The general notion of what is now called Hall algebra or Ringel-Hall algebra is an algebra defined out of a certain type of category, a "finitary abelian category". Finitary abelian categories are, roughly speaking, categories where the notions of exact sequences make sense and such that for any pair of objects A,B in the category in question, we have # Hom(A,B) <∞ and # Ext1(A,B) <∞. The Hall ...

A ‘resolution’ of the interior singularity of the spherically symmetric Schwarzschild solution of the Einstein equations for the gravitational field of a point-particle is carried out entirely and solely by finitistic and algebraic means. To this end, the background differential spacetime manifold and, in extenso, Calculus-free purely algebraic (:sheaf-theoretic) conceptual and technical machin...

In a simple CM-trivial theory every hyperimaginary is interbounded with a sequence of finitary hyperimaginaries. Moreover, such a theory eliminates hyperimaginaries whenever it eliminates finitary hyperimaginaries. In a supersimple CM-trivial theory, the independence relation is stable.

A ‘resolution’ of the interior singularity of the spherically symmetric Schwarzschild solution of the Einstein equations for the gravitational field of a point-particle is carried out entirely and solely by finitistic and algebraic means. To this end, the background differential spacetime manifold and, in extenso, Calculus-free purely algebraic (:sheaf-theoretic) conceptual and technical machin...

A ‘resolution’ of the interior singularity of the spherically symmetric Schwarzschild solution of the Einstein equations for the gravitational field of a point-particle is carried out entirely and solely by finitistic and algebraic means. To this end, the background differential spacetime manifold and, in extenso, Calculus-free purely algebraic (:sheaf-theoretic) conceptual and technical machin...

We construct from a finitary exact category with duality A a module over its Hall algebra, called the Hall module, encoding the first order self-dual extension structure ofA. We study in detail Hall modules arising from the representation theory of a quiver with involution. In this case we show that the Hall module is naturally a module over the specialized reduced σ-analogue of the quantum Kac...