In [2], Auslander and Smalø introduced and studied extensively preprojective modules and preinjective modules over an artin algebra. We now call a module hereditarily preprojective or hereditarily preinjective if its submodules are all preprojective or its quotient modules are all preinjective, respectively. In [4], Coelho studied Auslander-Reiten components containing only hereditarily preproj...

In 1967 Gurevich [3] published a proof that the class of divisible Axchimedean lat t ice-ordered abelian groups such that the lattice of carriers is an atomic Boolean algebra has a hereditarily undecidable first-order theory. (He essentially showed the reduct of this class to lattices has a hereditarily undecidable first-order theory: on p. 49 of his paper change z ~ u + v to z ~ u v v in the d...

Any hereditarily finite set S can be represented as a finite pointed graph –dubbed membership graph– whose nodes denote elements of the transitive closure of {S} and whose edges model the membership relation. Membership graphs must be hyper-extensional –nodes are pairwise not bisimilar– and bisimilar nodes represent the same hereditarily finite set. It is worth to notice that the removal of eve...

In this paper we answer a question of Wayne Lewis by proving that if X is a one-dimensional, hereditarily indecomposable continuum and if HX(X) is finitely generated, then C(X), the hyperspace of subcontinua of X, has dimension 2. Let C(A) be the hyperspace of subcontinua of the continuum X with the topology determined by the Hausdorff metric. A classical theorem of J. L. Kelley [4] asserts tha...

The study of relationships between structure and dynamics of asynchronous Boolean networks has recently led to the introduction of hereditarily bijective maps and even or odd self-dual networks. We show here that these two notions can be simply characterized geometrically: through orthogonality between certain affine subspaces. We also use this characterization to provide a construction of the ...

For a topological space X, let L(X) be the modal logic of X where is interpreted as interior (and hence ♦ as closure) in X. It was shown in [6] that the modal logics S4, S4.1, S4.2, S4.1.2, S4.Grz, S4.Grzn (n ≥ 1), and their intersections arise as L(X) for some Stone space X. We give an example of a scattered Stone space whose logic is not such an intersection. This gives an affirmative answer ...

Acknowledgments Obviously, though by no means trivially, many thanks are due to my advisor Professor Vincent Moulton, for introducing me to this fascinating subject, providing inspiration and helping me get started. Many thanks also to my colleague and co-author Dr. Katharina Huber for her patience during the many hours we spent going over the proofs in this paper. I am also most grateful to my...

The paper is organized as a self-contained literate Haskell program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic encodings. The code, tested under GHC 6.6.1, is available at http://logic.csci.unt.edu/tarau/ research/2008/fSET.zip. We introduce ranking and unranking functions generalizing Ackermann’s encoding to the universe of...

We prove that the hierarchy of hereditarily effective typestreams, that are effective models of inductivly defined types, has the length of the first recursivly inaccessible ordinal.

In [l] Bing constructed a 1-dimensional hereditarily indecomposable continuum which is the inverse limit of a sequence of circles Ct and such that the maps/*: C —>C;_i were of degree 1. In this paper we show that the dimension cannot be raised, i.e., if 5 = Lim(54 , /,-) where St is an TV-sphere and fi is essential, then 5 is not hereditarily indecomposable. In doing so we further generalize Bi...