We answer a question of Jockusch by constructing a hyperimmunefree minimal degree below a 1-generic one. To do this we introduce a new forcing notion called arithmetical Sacks forcing. Some other applications are presented.

In 1924 Libman and Sacks published an account of atypical, sterile, verrucous vegetations on the heart in systemic lupus erythematosus (SLE). [1] Clusters of verrucae, looking like mulberries, were described on the ventricular surface of the posterior leaflet of the mitral valve and found at postmortem. The leaflet and the chordae tendinae are often adherent to the endocardium of the ventricula...

We consider a cardinal invariant closely related to Hindman’s theorem. We prove that this cardinal invariant is small in the iterated Sacks perfect set forcing model, and that its corresponding parametrized diamond principle implies the existence of union ultrafilters. As a corollary, this establishes the existence of union ultrafilters in the iterated Sacks model of Set Theory.

Libman-Sacks endocarditis is a classic but rarely symptomatic manifestation of systemic lupus erythematosus, and valvular surgery is needed in a few cases. We present a patient with systemic lupus erythematosus and Libman-Sacks endocarditis that progressed rapidly to severe mitral regurgitation that needed surgery; surgical valve repair was decided upon. The literature on this topic is reviewed.

Rational numbers are used to classify maximal almost disjoint (MAD) families of subsets of the integers. Combinatorial characterization of indestructibility of MAD families by the likes of Cohen, Miller and Sacks forcings are presented. Using these it is shown that Sacks indestructible MAD family exists in ZFC and that b = c implies that there is a Cohen indestructible MAD family. It follows th...

As in the traditional production of cheese in lambskin sacks raw cow's or sheep's milk is mostly used, the purpose of this study is to see how the production affects the microbiological quality of the cheese. To do that, we tested 39 samples of raw cow's and sheep's milk, curd, ripened cheese (15, 30 and 45 days) and lambskin sacks for native microbial population. Two-thirds of the milk, curd a...

Lord Rabbi Sacks was a major religious Jewish figure. In this article, we examine his version of covenant-based communitarianism. We begin with exploring Sacks’ social communitarian view, and support politics. then turn to evaluate argue that while view is valuable important, political faces the same challenges troubled views, namely fact religious, value, ethnic plurality. One possible way for...