Download A theorem of Eliashberg and Thurston on foliations and by Carlo Petronio PDF

By Carlo Petronio

Those notes originate from a seminar held in Pisa in November and December 1996 together by way of Riccardo Benedetti, Paolo Lisca and me. the purpose of those notes is to provide a close facts of the next consequence because of Eliashberg and Thurston: THM allow M be a closed orientated 3-manifold and allow F be a cooriented C2-smooth codimension-1 foliation on M. imagine that (M,F) isn't diffeomorphic to the product foliation on S2xS1. Then arbitrarily as regards to F within the C0 topology there exist a good and a destructive C\infty touch constitution.

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329). The interpretivists call this set of principles a ‘universal grammar’. Just as a transformational grammar was an abstract set of rules that characterized an individual language, the universal grammar is an abstract set of rules that characterizes transformational grammars. That is, it describes which trans- Response to Dresher and Hornstein 137 formational grammars may be constructed, and which may not. The transformationalists feel that such a set of rules is explanatory, because it explains how any given transformational grammar is possible.

130 Dean Delis and Anne Saxon Slater enabling them to communicate the same propositions as when reduction rules are not employed, but with redundant information deleted. When the communicative setting of the experiment specified that the designated addressees would easily comprehend the base propositions, the subjects elected to use a much higher percentage of reduction transformations than when the setting specified that the addressess would have difficulty in comprehending the propositions. Thus, in general, the experiment demonstrated that a relationship exists between the transformational histories of sentences and (1) the conceptual background shared by language users, and (2) factors inherent in the way human beings communicate and comprehend information.

What we do have is a number of competing theories, each of which accounts for some aspects of language use better than the others. Given that our problem is not one of choosing from among a number of adequate theories, but to define the limits and failings of existing theories, some sort of experimental methodology is needed. In this respect, AI methodology - that is, building a program as a test of theory ~ has been extremely useful in pointing out deficiencies of theories, and uncovering problems that were not well understood beforehand.

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