[E1] Recurrent points and hyperarithmetic sets In: Set Theory, Techniques and Applications, Curacao 1995 and Barcelona 1996 conferences, edited by C. A. Di Prisco, Jean A. Larson, Joan Bagaria and A. R. D. Mathias, Kluwer Academic Publishers, Dordrecht, Boston, London, 1998, 157--174.) .ps.dvi

(really a scholium to [E2], though published sooner; gives an example of a recursively defined iteration that stabilises at the first non-recursive ordinal, and suggests approaches to a conjecture that was later refuted in [E5], though some of the ideas survive in [E3] and [E4].)

(using set-theoretical ideas to study the iteration of derived ω-limit sets in dynamical systems, proves that, from every starting point, that iteration stabilises not later than the first uncountable ordinal, gives examples in Baire and in Cantor space for each countable ordinal of iterations lasting exactly that long, gives an example of a recursively defined point starting from which the iteration stabilises at the first non-recursive ordinal, and gives new examples of complete analytic sets.)

[E3] Choosing an attacker by a local derivation Acta Universitatis Carolinae - Math. et Phys., 45 (2004) 59--65. .ps .dvi

(the surviving fragment of attempts to prove the conjectures refuted in [E5].)

(gives a sufficient condition for a dynamical system to contain a point of uncountable score.)

[E5] Analytic sets under attack Math. Proc. Cam. Phil. Soc. 138 '2005) 465--485; MR 2138574 .ps.dvi

(answers questions left open in "Delays" by constructing two recursive points, a and b , in Baire space such that the second derived ω-limit set starting from a is a complete analytic set whilst the third is empty, whereas starting from the point b the iteration of derived ω-limit sets stabilises exactly at the first uncountable ordinal, yielding yet another complete analytic set.)