The strength of countable saturation

We determine the proof-theoretic strength of the principle of countable saturation in the context of the systems for nonstandard arithmetic introduced in our earlier work.Comment: Corrected typos in Lemma 3.4 and the final paragraph of the conclusio

The Tissue Kallikrein Family of Serine Proteases: Functional Roles in Human Disease and Potential as Clinical Biomarkers

Prostate specific antigen (PSA) or human kallikrein 3 (hK3) has long been an effective biomarker for prostate cancer. Now, other members of the tissue kallikrein (KLK) gene family are fast becoming of clinical interest due to their potential as prognostic biomarkers, particularly for hormone dependent cancers. The tissue kallikreins are serine proteases that are encoded by highly conserved multi-gene family clusters in rodents and humans. The rat and mouse loci contain 10 and 25 functional genes, respectively, while the human locus at 19q 13.4 contains 15 genes. The structural organization and size of these genes are similar across species; all genes have 5 coding exons that encode a prepro-enzyme. Although the physiological activators of these zymogens have not been described, in vitro biochemical studies show that some kallikreins can auto-activate and others can activate each other, suggesting that the kallikreins may participate in an enzymatic cascade similar to that of the coagulation cascade. These genes are expressed, to varying degrees, in a wide range of tissues suggesting a functional involvement in a diverse range of physiological and pathophysiological processes. These include roles in normal skin desquamation and psoriatic lesions, tooth development, neural plasticity, and Alzheimer's disease (AD). Of particular interest is the expression of many kallikreins in prostate, ovarian, and breast cancers where they are emerging as useful prognostic indicators of disease progression