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 study the frequency of hypercyclicity of hypercyclic, non–weakly mixing linear operators. In particular, we show that on the space `(N), any sublinear frequency can be realized by a non–weakly mixing operator. A weaker but similar result is obtained for c0(N) or `(N), 1 < p <∞. Part of our results is related to some Sidon-type lacunarity properties for sequences of natural numbers.

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...

We give a sufficient condition for two operators to be disjointly frequently hypercyclic. apply this criterion composition acting on H(D) or the Hardy space H2(D). simplify result disjoint frequent hypercyclicity of pseudo shifts recent paper Martin et al. and we exhibit hypercyclic weighted shifts.

A cardinal λ is called ω-inaccessible if for all μ < λ we have μ < λ. We show that for every ω-inaccessible cardinal λ there is a CCC (hence cardinality and cofinality preserving) forcing that adds a hereditarily Lindelöf regular space of density λ. This extends an analogous earlier result of ours that only worked for regular λ. In [1] we have shown that for any cardinal λ a natural CCC forcing...