Related papers: A Report on Realizability
The complexity of equivalence relations has received much attention in the recent literature. The main tool for such endeavour is the following reducibility: given equivalence relations $R$ and $S$ on natural numbers, $R$ is computably…
Analytic-bilinear approach for construction and study of integrable hierarchies, in particular, the KP hierarchy is discussed. It is based on the generalized Hirota identity. This approach allows to represent generalized hierarchies of…
Using a result of Vdovina, we may associate to each complete connected bipartite graph $\kappa$ a $2$-dimensional square complex, which we call a tile complex, whose link at each vertex is $\kappa$. We regard the tile complex in two…
We study approximations of compact linear multivariate operators defined over Hilbert spaces. We provide necessary and sufficient conditions on various notions of tractability. These conditions are mainly given in terms of sums of certain…
Geometric morphisms between realizability toposes are studied in terms of morphisms between partial combinatory algebras (pcas). The morphisms inducing geometric morphisms (the {\em computationally dense\/} ones) are seen to be the ones…
Reachability logic has been applied to $\mathbb{K}$ rewrite-rule-based language definitions as a language-generic logic of programs. To be able to verify not just code but also distributed system designs, a new rewrite-theory-generic…
This article is Part I in a series of three papers devoted to determining the minimal complexity of scales in the inner model $K(\mathbb{R})$. Here, in Part I, we shall complete our development of a fine structure theory for $K(\mathbb{R})$…
We prove that the existence of finite combinatorial objects such as affine planes, mutually orthogonal Latin squares, and resolvable balanced incomplete block designs can be reformulated as the existence of certain algorithmic reductions…
We use the technique of "classical realizability" to build new models of ZF + DC in which R is not well ordered. This gives new relative consistency results, probably not obtainable by forcing. This gives also a new method to get programs…
We build models using an indiscernible model sub-structures of ${\kappa} \ge {\lambda}$ and related more complicated structures. We use this to build various Boolean algebras.
We shall generalize the notion of a Laver table to algebras which may have many generators, several fundamental operations, fundamental operations of arity higher than 2, and to algebras where only some of the operations are…
We propose for the Effective Topos an alternative construction: a realisability framework composed of two levels of abstraction. This construction simplifies the proof that the Effective Topos is a topos (equipped with natural numbers),…
Let $K$ be a field, and $A=K[a_1,\ldots ,a_n]$ a solvable polynomial algebra in the sense of [K-RW, {\it J. Symbolic Comput.}, 9(1990), 1--26]. Based on the Gr\"obner basis theory for $A$ and for free modules over $A$, an elimination theory…
Tracial Rokhlin property was introduced by Chris Phillips to study the structure of crossed product of actions on simple C*-algebras. It was originally defined for actions of finite groups and group of integers. Matui and Sato generalized…
A series of vertex operator algebras are constructed by GKO-construction, which is a generalization of 3A-algebra and 6A-algebra. It is proved their vertex operator algebra structures are unique under nonzero assumptions on some elements of…
We consider algebras of languages over the signature of reversible Kleene lattices, that is the regular operations (empty and unit languages, union, concatenation and Kleene star) together with intersection and mirror image. We provide a…
The TTE approach to Computable Analysis is the study of so-called representations (encodings for continuous objects such as reals, functions, and sets) with respect to the notions of computability they induce. A rich variety of such…
Provability logic GLP is well-known to be incomplete w.r.t. Kripke semantics. A natural topological semantics of GLP interprets modalities as derivative operators of a polytopological space. Such spaces satisfying all the axioms of GLP are…
The modern algebra concepts are used to construct tables of algebraic spinors related to Clifford algebra multivectors with real and complex coefficients. The following data computed by Mathematica are presented in form of tables for…
An equivalence between generalised restricted solid-on-solid (RSOS) models, associated with sets of graphs, and multi-colour loop models is established. As an application we consider solvable loop models and in this way obtain new solvable…