Assuming AD + (V = L(R)), it is shown that for κ an admissible Suslin cardinal, o(κ) (= the order type of the stationary subsets of κ) is "essentially" regular and closed under ultrapowers in a manner to be made precise. In particular, o(κ) ≫ κ +, κ ++ , etc. It is conjectured that this characterizes admissibility for L(R).

We formulate and prove a combinatorial property assuming AD + V = L(R). As a consequence, we show that every regular κ which is either a Suslin cardinal or the successor of a Suslin cardinal is δ 2 1 -supercompact. In particular, all the projective ordinals δ 1 n are δ 2 1 -supercompact.

Science studies has long been concerned with the theoretical and methodological challenge of mess—the inevitable tendency of technoscientific objects and practices to spill beyond the neat analytic categories we construct for them. Nowhere is this challenge greater than in the messy world of large-scale collaborative science projects, particularly though not exclusively in their start-up phases. This article examines the complicated life and death of the WATERS Network, an ambitious and ultimately abandoned effort at collaborative infrastructure development among hydrologists, engineers, and (...) social scientists studying water. We argue in particular against the “forensic imagination,” a particular style of accounting for failure in the messy world of large-scale network development, and against two common conceptual and empirical pitfalls that it gives rise to: defaults to formalism and defaults to the future. We argue that alternative postforensic approaches to “failures” like the WATERS Network can support forms of learning and accountability better attuned to the complexities of practice and policy in the real world of scientific collaboration and network formation. (shrink)

We work under the assumption of the Axiom of Determinacy and associate a measure to each cardinal $\kappa < \aleph_{\varepsilon_0}$ in a recursive definition of a canonical measure assignment. We give algorithmic applications of the existence of such a canonical measure assignment (computation of cofinalities, computation of the Kleinberg sequences associated to the normal ultrafilters on all projective ordinals).

Let E be a coanalytic equivalence relation on a Polish space X and (A n ) n∈ω a sequence of analytic subsets of X. We prove that if lim sup n∈K A n meets uncountably many E-equivalence classes for every K ∈ [ω] ω , then there exists a K ∈ [ω] ω such that ⋂ n∈K A n contains a perfect set of pairwise E-inequivalent elements.

We survey some results and problems arising from a classic problem of Steinhaus: Is there a subset S of R 2 such that each isometric copy of mathbbZ 2 (the lattice points in the plane) meets S in exactly one point.

We show that all the projective ordinals $\delta^1_n$ are supercompact through their supremum $\aleph_{\varepsilon 0}$, and a ways beyond.

Let X and Y be uncountable Polish spaces. We show in ZF that there is a coanalytic subset P of X × Y with countable sections which cannot be expressed as the union of countably many partial coanalytic, or even PCA = Σ 1 2 , graphs. If X = Y = ω ω , P may be taken to be Π 1 1 . Assuming stronger set theoretic axioms, we identify the least pointclass such that any such coanalytic P (...) can be expressed as the union of countably many graphs in this pointclass. This last result is extended (under suitable hypotheses) to all levels of the projective hierarchy. (shrink)