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2 results

  • 18 - The Ulm and Austerlitz Campaigns, 1805

  • from Part IV - Napoleon’s Military Campaigns in Europe
  • Edited by Bruno Colson, Alexander Mikaberidze, Louisiana State University, Shreveport
  • Book:
    The Cambridge History of the Napoleonic Wars
    Published online:
    20 December 2022
    Print publication:
    02 March 2023, pp 355-380

  • Summary

    The chapter discusses the events of the War of the Third Coalition that climaxed on the field of Austerlitz in one of the most famous battles in military history. The 1805 Campaign was the first one Napoleon fought as the emperor and it consolidated his martial reputation: a classic example of the general’s logistical and operational brilliance that allowed him to outmarch and outfight his enemy in just three months after the start of the war. Beginning with the bold and rapid advance of the French Army from the Rhine to the Danube, the chapter examines Napoleon’s envelopment of the Austrian army at Ulm, the manoeuvres to Austerlitz and the counter-attack that resulted in the decisive defeat for the Austro-Russian Army.

  • The isomorphism problem for computable Abelian p-groups of bounded length

  • Wesley Calvert
  • Journal:
    The Journal of Symbolic Logic / Volume 70 / Issue 1 / March 2005
    Published online by Cambridge University Press:
    12 March 2014, pp. 331-345
    Print publication:
    March 2005

  • Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider only countable members. This paper explores such a notion for classes of computable structures by working out a sequence of examples.

    We follow recent work by Goncharov and Knight in using the degree of the isomorphism problem for a class to distinguish classifiable classes from non-classifiable. In this paper, we calculate the degree of the isomorphism problem for Abelian p-groups of bounded Ulm length. The result is a sequence of classes whose isomorphism problems are cofinal in the hyperarithmetical hierarchy. In the process, new back-and-forth relations on such groups are calculated.