A generalization of Quillen's small object argument

We generalize the small object argument in order to allow for its application to proper classes of maps (as opposed to sets of maps in Quillen's small object argument). The necessity of such a generalization arose with appearance of several important examples of model categories which were proven to be non-cofibrantly generated. Our current approach allows for construction of functorial factorizations and localizations in the equivariant model structures on diagrams of spaces and diagrams of chain complexes. We also formulate a non-functorial version of the argument, which applies in two different model structures on the category of pro-spaces. The examples above suggest a natural extension of the framework of cofibrantly generated model categories. We introduce the concept of a class-cofibrantly generated model category, which is a model category generated by classes of cofibrations and trivial cofibrations satisfying some reasonable assumptions.Comment: 14 pages. The paper is substantially revisited. Another (non-functorial) version of the argument discussed. New examples added. The claim about functoriality of factorizations in the category of pro-spaces is withdraw

An example of a non-cofibrantly generated model category

We show that the model category of diagrams of spaces generated by a proper class of orbits is not cofibrantly generated. In particular the category of maps between spaces may be given a non-cofibrantly generated model structure.Comment: 4 pages, AMS-LaTeX2

The effect of accountability policies in primary education in Amsterdam

This paper assesses the increase in test scores of educational achievements in primary schools in Amsterdam by analyzing data of a large sample of schools, including scores on a published test and scores on similar independently taken tests that are not published. In 1995, the municipality of Amsterdam introduced accountability policies for schools in primary education. Population statistics show a large increase of test scores in the decade after the introduction of the policies. Difference-in-differences estimates show that after the introduction of the accountability policies, test scores for both tests taken in grade 8 increased substantially more in Amsterdam than in the rest of the country and more than in a sample of pupils with a low socio-economic status. Approximately 60 percent of the increase of the published test scores can be attributed to an increase in general skills and 40 percent to an increase in test-specific skills. Test scores of pupils in lower grades also improved in Amsterdam. We do not find evidence for strategic behavior of schools. Although part of the gains in test scores might be test-specific, the accountability policies in Amsterdam seem to have succeeded in raising educational achievements in primary schools.