We study the logic obtained by endowing the language of first-order arithmetic with second-order measure quantifiers. This new kind of quantification allows us to express that the argument formula is true in a certain portion of all possible interpretations of the quantified variable. We show that first-order arithmetic with measure quantifiers is capable of formalizing simple results from probability theory and, most importantly, of representing every recursive random function. Moreover, we introduce a realizability interpretation of this logic in which programs have access to an oracle from the Cantor space.

Superior vena cava (SVC) occlusion can be clinically recognized in the acute setting when the stenosing process does not allow the development of collateral venous channels, which guarantee the venous drainage to the right heart. On the contrary, when the obstruction develops progressively, the diagnosis of SVC obstruction may remain undiagnosed. In the present case, the presence of SVC thrombosis was purely coincidental. In fact, the obstruction was first noticed on diagnostic tests performed because of the malfunction of a totally implantable Porth a Cath placed into the superior vena cava (through right subclavian access), five years before, in a patient suffering from non-Hodgkin disease. Venography is the most appropriate diagnostic methodology which reveals the presence of a dilated azygos vein as a compensatory mechanism. Comparison with computed tomography allows to confirm the diagnosis and to identify the possible causes. Dilatation of the azygos vein, secondary to superior vena cava thrombosis, although a rare event, should be taken into consideration in those patients with CVC and who present with frequent episodes of deep venous thrombosis.

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