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We show that there are no infinite maximal almost disjoint ("mad") families in Solovay's model, thus solving a long-standing problem posed by A.D.R. Mathias in 1967. We also give a new proof of Mathias' theorem that no analytic infinite almost disjoint family can be maximal, and show more generally that if Martin's Axiom holds at $\kappa<2^{\aleph_0}$, then no $\kappa$-Souslin infinite almost disjoint family can be maximal. Finally we show that if $\aleph_1^{L[a]}<\aleph_1$, then there are no $\Sigma^1_2[a]$ infinite mad families., Comment: Changes in version 2: (1) The proof of Claim 2 on p. 9 has been fixed. (2) Notation regarding characteristic functions and the sets they define has been explained more clearly (3) Typos corrected throughout the manuscript

We consider natural $\Sigma^1_2$ definable analogues of many of the classical statements that have been shown to be equivalent to CH. It is shown that these $\Sigma^1_2$ analogues are equivalent to that all reals are constructible. We also prove two partition relations for $\Sigma^1_2$ colourings which hold precisely when there is a non-constructible real., Comment: Several minor corrections throughout. Finally submitted

We prove that for a countable discrete group $\Gamma$ containing a copy of the free group $\F_n$, for some $2\leq n\leq\infty$, as a normal subgroup, the equivalence relations of conjugacy, orbit equivalence and von Neumann equivalence of the ergodic a.e. free actions of $\Gamma$ are analytic non-Borel equivalence relations in the Polish space of probability measure preserving $\Gamma$ actions. As a consequence we obtain that the isomorphism relation in the spaces of separably acting factors of type $\II_1$, $\II_\infty$ and $\III_\lambda$, $0\leq\lambda\leq 1$, are analytic and not Borel when these spaces are given the Effros Borel structure., Comment: 28 pages. Minor corrections throughout

We study maximal orthogonal families of Borel probability measures on $2^\omega$ (abbreviated m.o. families) and show that there are generic extensions of the constructible universe $L$ in which each of the following holds: (1) There is a $\Delta^1_3$-definable well order of the reals, there is a $\Pi^1_2$-definable m.o. family, there are no $\mathbf{\Sigma}^1_2$-definable m.o. families and $\mathfrak{b}=\mathfrak{c}=\omega_3$ (in fact any reasonable value of $\mathfrak{c}$ will do). (2) There is a $\Delta^1_3$-definable well order of the reals, there is a $\Pi^1_2$-definable m.o. family, there are no $\mathbf{\Sigma}^1_2$-definable m.o. families, $\mathfrak{b}=\omega_1$ and $\mathfrak{c}=\omega_2$., Comment: 12 pages

We bound the Borel cardinality of the isomorphism relation for nuclear simple separable C*-algebras: It is turbulent, yet Borel reducible to the action of the automorphism group of the Cuntz algebra O_2 on its closed subsets. The same bounds are obtained for affine homeomorphism of metrizable Choquet simplexes. As a by-product we recover a result of Kechris and Solecki, namely, that homeomorphism of compacta in the Hilbert cube is Borel reducible to a Polish group action. These results depend intimately on the classification theory of nuclear simple C*-algebras by K-theory and traces. Both of necessity and in order to lay the groundwork for further study on the Borel complexity of C*-algebras, we prove that many standard C*-algebra constructions and relations are Borel, and we prove Borel versions of Kirchberg's O_2-stability and embedding theorems. We also find a C*-algebraic witness for a K_\sigma hard equivalence relation., Comment: 42 pages, largely minor changes with the exception of a corrected 4.4

We show that the unitary conjugacy relation for unitary representations of a second countable locally compact group on a separable Hilbert space is a Borel equivalence relation., Comment: 11 pages. Submitted

In this paper we show that there are "E_0 many" orbit inequivalent free actions of the free groups F_n, $2\leq n\leq\infty$, by measure preserving transformations on a standard Borel probability space. In particular, there are uncountably many such actions., Comment: This paper appeared in the Journal of Symbolic Logic, see reference below. (Nov. 29: Title of paper corrected.)

Using Baire category techniques we prove that Araki-Woods factors are not classifiable by countable structures. As a result, we obtain a far reaching strengthening as well as a new proof of the well-known theorem of Woods that the isomorphism problem for ITPFI factors is not smooth. We derive as a consequence that the odometer actions of Z that preserve the measure class of a finite non-atomic product measure are not classifiable up to orbit equivalence by countable structures., Comment: 16 pages

We show that the continuum hypothesis implies that every measure preserving near-action of a group on a standard Borel probability space $(X,\mu)$ has a pointwise implementation by Borel measure preserving automorphisms., Comment: Numerous typos corrected

We announce some new results regarding the classification problem for separable von Neumann algebras. Our results are obtained by applying the notion of Borel reducibility and Hjorth's theory of turbulence to the isomorphism relation for separable von Neumann algebras.

We prove that if $V=L$ then there is a $\Pi^1_1$ maximal orthogonal (i.e. mutually singular) set of measures on Cantor space. This provides a natural counterpoint to the well-known Theorem of Preiss and Rataj that no analytic set of measures can be maximal orthogonal., Comment: Minor corrections in the proof of the main theorem

The study of Borel equivalence relations under Borel reducibility has developed into an important area of descriptive set theory. The dichotomies of Silver and Harrington-Kechris-Louveau show that with respect to Borel reducibility, any Borel equivalence relation strictly above equality on $\omega$ is above equality on ${\cal P}(\omega)$, the power set of $\omega$, and any Borel equivalence relation strictly above equality on the reals is above equality modulo finite on ${\cal P}(\omega)$. In this article we examine the effective content of these and related results by studying effectively Borel equivalence relations under effectively Borel reducibility. The resulting structure is complex, even for equivalence relations with finitely many equivalence classes. However use of Kleene's $O$ as a parameter is sufficient to restore the picture from the noneffective setting. A key lemma is the existence of two effectively Borel sets of reals, neither of which contains the range of the other under any effectively Borel function; the proof of this result applies Barwise compactness to a deep theorem of Harrington establishing for any recursive ordinal $\alpha$ the existence of $\Pi^0_1$ singletons whose $\alpha$-jumps are Turing incomparable.

We prove that it is not possible to classify separable von Neumann factors of types $\II_1$, $\II_\infty$ or $\III_\lambda$, $0\leq \lambda\leq1$, up to isomorphism by a Borel measurable assignment of "countable structures" as invariants. In particular the isomorphism relation of type $\II_1$ factors is not smooth. We also prove that the isomorphism relation for von Neumann $\II_1$ factors is analytic, but is not Borel., Comment: To appear in the Journal of Functional Analysis

We prove the following analogue of a Theorem of R.O. Davies: Every $\Sigma^1_2$ function $f:\R\times\R\to\R$ can be represented as a sum of rectangular $\Sigma^1_2$ functions if and only if all reals are constructible., Comment: Final version, to appear in Fundamenta Mathematicae

We prove that orbit equivalence of measure preserving ergodic a.e. free actions of a countable group with the relative property (T) is a complete analytic equivalence relation., Comment: Final version, to appear in the Israel Journal of Mathematics

We prove that if $G$ is a countable discrete group with property (T) over an infinite subgroup $H

A study was done of the transfer of knowledge between academic and firm scientists. Beginning with theories of university and university scientist behavior and a theory of firm and firm scientist behavior, the research used a bibliometric analysis of articles prepared by firm-based scientists within the computer equipment and aircraft industries. Preliminary results indicate that the rate of university collaboration by firms in these industries is 12 percent and that the rate of utilization of university research is 43 percent with university-based publications the most heavily cited of all author affiliation categories. University collaboration and utilization varied across industries and by firm size: the computer equipment industry had four times as many actively publishing firms as the aircraft industry. While individual article characteristics consistently had predictive value for firm publication practices, proximity to university research did not. In addition, industrial research drew on university produced papers more frequently for theoretical research than for applied work. Larger firms used university research, and produced and used theoretical work more often than smaller firms while papers reflecting applied research were more often produced by smaller firms. Included are extensive tables of data in an appendix and 51 references. (JB)

A study used publication statistics to investigate the collaboration and research use of scientists in the computer equipment and aircraft industries. Results reveal that these industries are using research generated by university scientists, and that collaboration between sectors is occurring. Geographic proximity is linked to increased collaboration, suggesting local efforts may be fruitful for institutions. (Author/MSE)

Citation analysis of 92 articles published about the aircraft and electronic equipment industries investigated the higher education institutions with which cited authors were associated. Results indicated research expenditures, faculty quality and salary, and land-grant status were predictors of research use; urban location and presence of cooperative research structures were not. (MSE)