We introduce the notion of infinitary interpretation of structures. In general, an interpretation between structures induces a continuous homomorphism between their automorphism groups, and furthermore, it induces a functor between the categories of copies of each structure. We show that for the case of infinitary interpretation the reversals are also true: Every Baire-measurable homomorphism b...

The notions of quasi-prime submodules and developed  Zariski topology was introduced by the present authors in cite{ah10}. In this paper we use these notions to define a scheme. For an $R$-module $M$, let $X:={Qin qSpec(M) mid (Q:_R M)inSpec(R)}$. It is proved that $(X, mathcal{O}_X)$ is a locally ringed space. We study the morphism of locally ringed spaces induced by $R$-homomorphism $Mrightar...

For any two graphs F and G, let hom(F,G) denote the number of homomorphisms F → G, that is, adjacency preserving maps V (F ) → V (G) (graphs may have loops but no multiple edges). We characterize Institute of Mathematics, Eötvös Loránd University, Budapest, Hungary. Email: [email protected]. Research sponsored by OTKA Grant No. 67867. CWI and University of Amsterdam, Amsterdam, The Netherlands....

For a fixed graph H, we consider the H-Recoloring problem : given a graph G and two H-colorings of G, i.e., homomorphisms from G to H, can one be transformed into the other by changing one color at a time, maintaining an H-coloring throughout. This is the same as finding a path in the Hom(G,H) complex. For H = Kk this is the problem of finding paths between k-colorings, which was recently shown...