We show that if the weak compactness of a cardinal is made indestructible by means of any preparatory forcing of a certain general type, including any forcing naively resembling the Laver preparation, then the cardinal was originally supercompact. We then apply this theorem to show that the hypothesis of supercompactness is necessary for certain proof schemata.

First Published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

It is widely agreed that a new conception of history was developed in the early nineteenth century: the past came to be seen in a new light, as did the way of studying the past. This article discusses the nature of this collective revision, focusing on one of its first and most important manifestations: Ranke's 1824 Geschichten der romanischen und germanischen Völker. It argues that, in Ranke's case, the driving force of the revision was religious, and that, subsequently, an understanding (...) of the nature of Ranke's religious attitude is vital to any interpretation of his historical revision. Being aesthetic-experiential rather than conceptual or "positive," this religious element is reflected throughout Ranke's enterprise, in source criticism and in historical representation no less than in the conception of cause and effect in the historical process. These three levels or aspects of the historical enterprise correspond to the experience of the past, and are connected by the essence of the experience: visual perception. The highly individual character of the enterprise, its foundation in sentiments and experiences of little persuasive force that only with difficulty can be brought into language at all, explains the paradoxical nature of the Rankean heritage. On the one hand, Ranke had a great and lasting impact; on the other hand, his approach was never re-utilized as a whole, only in its constituent parts—which, when not in the relationship Ranke had envisioned, took on a new and different character. This also suggests the difference between Ranke's revision and a new paradigm: whereas the latter is an exemplary solution providing binding regulations, the former is unrepeatable. (shrink)

The focus of this study was to analyze the content, distribution, and comparative genome relationships of 996 chromosome bin-mapped expressed sequence tags accounting for 2266 restriction fragments on the homoeologous group 3 chromosomes of hexaploid wheat. Of these loci, 634, 884, and 748 were mapped on chromosomes 3A, 3B, and 3D, respectively. The individual chromosome bin maps revealed bins with a high density of mapped ESTs in the distal region and bins of low density in the proximal region of the (...) chromosome arms, with the exception of 3DS and 3DL. These distributions were more localized on the higher-resolution group 3 consensus map with intermediate regions of high-mapped-EST density on both chromosome arms. Gene ontology classification of mapped ESTs was not significantly different for homoeologous group 3 chromosomes compared to the other groups. A combined analysis of the individual bin maps using 537 of the mapped ESTs revealed rearrangements between the group 3 chromosomes. Approximately 232 of the consensus mapped ESTs matched sequences on rice chromosome 1 and revealed large- and small-scale differences in gene order. Of the group 3 mapped EST unigenes ∼21 and 32% matched the Arabidopsis coding regions and proteins, respectively, but no chromosome-level gene order conservation was detected. (shrink)

We discuss the question of Ralf-Dieter Schindler whether for infinite time Turing machines Pf = NPf can be true for any function f from the reals into ω1. We show that “almost everywhere” the answer is negative.

One third of the transcendental dialectic in Kant's Critique of Pure Reason is devoted to demolishing the pseudo-science of rational psychology. In this part of his work Kant attacks the idea that there is an ultimate subject of experience — the ‘I’ or Self — which can only be investigated and understood intellectually. The belief that such a study is possible is natural to human reason; but it is based on demonstrable error. Kant tries to exorcize our minds from falling (...) prey to this mistake. (shrink)