Where There Are Not Enough Doctors

How many doctors are enough?

obesity dilemma: are there enough bariatric surgeons?

Are There Enough Injective Sets?

The axiom of choice ensures precisely that, in ZFC, every set is projective: that is, a projective object in the category of sets. In constructive ZF (CZF) the existence of enough projective sets has been discussed as an additional axiom taken from the interpretation of CZF in Martin-Löf’s intuitionistic type theory. On the other hand, every non–empty set is injective in classical ZF, which arg...

Not Enough There There Evidence, Reasons, and Language Independence

The philosophical significance of language dependence results (à la Goodman’s “grue” problem) has been seriously underestimated. In this article I argue that: The trouble caused by language dependence is not confined to formal analyses of evidential support; language dependence concerns apply to any story about how we should draw conclusions from evidence. This is because language dependence re...

There Are Enough Azumaya Algebras on Surfaces

Using Maruyama’s theory of elementary transformations, I show that the Brauer group surjects onto the cohomological Brauer group for separated geometrically normal algebraic surfaces. As an application, I infer the existence of nonfree vector bundles on proper normal algebraic surfaces.