
7The Strange Logic of Random GraphsSpringer Verlag. 2001.The study of random graphs was begun in the 1960s and now has a comprehensive literature. This excellent book by one of the top researchers in the field now joins the study of random graphs (and other random discrete objects) with mathematical logic. The methodologies involve probability, discrete structures and logic, with an emphasis on discrete structures.

Finite model theory and its applications. Texts in Theoretical Computer ScienceBulletin of Symbolic Logic 16 (3): 406407. 2010.

18Saharon Shelah. Primitive recursive bounds for van der Waerden numbers. Journal of the American Mathematical Society, vol. 1 , pp. 683–697 (review)Journal of Symbolic Logic 55 (2): 887888. 1990.

5A covering design, or covering, is a family of ksubsets, called blocks, chosen from a vset, such that each tsubset is contained in at least one of the blocks. The number of blocks is the covering's size}, and the minimum size of such a covering is denoted by C. It is easy to see that a covering must contain at least / blocks, and in 1985 R\"odl [European J. Combin. 5, 6978] proved a longstanding conjecture of Erd\H{o}s and Hanani [Publ. Math. Debrecen 10, 1013] that for fixed k and t, cove…Read more

12Review: Saharon Shelah, Primitive Recursive Bounds for Van der Waerden Numbers (review)Journal of Symbolic Logic 55 (2): 887888. 1990.

17The complexity of random ordered structuresAnnals of Pure and Applied Logic 152 (13): 174179. 2008.We show that for random bit strings, Up, with probability, image, the first order quantifier depth D) needed to distinguish nonisomorphic structures is Θ, with high probability. Further, we show that, with high probability, for random ordered graphs, G≤,p with edge probability image, D)=Θ, contrasting with the results for random graphs, Gp, given by Kim et al. [J.H. Kim, O. Pikhurko, J. Spencer, O. Verbitsky, How complex are random graphs in first order logic? Random Structures and Algorithms 2…Read more

24Succinct definitions in the first order theory of graphsAnnals of Pure and Applied Logic 139 (1): 74109. 2006.We say that a first order sentence A defines a graph G if A is true on G but false on any graph nonisomorphic to G. Let L ) denote the minimum length of such a sentence. We define the succinctness function s ) to be the minimum L ) over all graphs on n vertices.We prove that s and q may be so small that for no general recursive function f we can have f)≥n for all n. However, for the function q*=maxi≤nq, which is the least nondecreasing function bounding q from above, we have q*=)log*n, where lo…Read more

555This Master of Arts thesis is in two parts: a novel, An Anarchy of Man, and an exegesis which places the novel in relation to philosophical concerns about the self and the way those concerns are portrayed in selected works of Western literature. The novel is set in Canberra and Sydney and tells the story of the relationship between two characters: Joe and Gin. It explores the way we in the modern Western world think about ourselves and those around us. Chapter One considers the view of the self …Read more