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A general extension theorem for directed-complete partial orders

Schuster P., Wessel D.

Reports on Mathematical Logic

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2018

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Vol. 53

79--96

EN

The typical indirect proof of an abstract extension theorem, by the Kuratowski-Zorn lemma, is based on a onestep extension argument. While Bell has observed this in case of the axiom of choice, for subfunctions of a given relation, we now consider such extension patterns on arbitrary directed-complete partial orders. By postulating the existence of so-called total elements rather than maximal ones, we can single out an immediate consequence of the Kuratowski-Zorn lemma from which quite a few abstract extension theorems can be deduced more directly, apart from certain definitions by cases. Applications include Baer’s criterion for a module to be injective. Last but not least, our general extension theorem is equivalent to a suitable form of the Kuratowski-Zorn lemma over constructive set theory.

2

The weak König Lemma, Brouwer fan theorem, De Morgan's Law, and dependent choice

Berger J., Ishihara H., Schuster P.

Reports on Mathematical Logic

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2012

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Vol. 47

63-86

EN

The standard omniscience principles are interpreted in a systematic way within the context of binary trees. With this dictionary at hand we revisit the weak König lemma (WKL) and Brouwer's fan theorem (FAN). We first study how one can arrive from FAN at WKL, and then give a direct decomposition, without coding, of WKL into the lesser limited principle of omniscience and an instance of the principle of dependent choices. As a complement we provide, among other equivalents of the standard omniscience principles, a uniform method to formulate most of them.

3

Improving the mechanical properties of braided shape memory polymer stents by heat setting

Schreiber F., Schuster P., Borinski M., Vogt F., Blindt R., Gries T.

Autex Research Journal

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2010

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Vol. 10, no. 3

73--76

EN

The aging population is one of the biggest challenges of the 21st century and so is the subsequent increase in patients with cardiovascular diseases. The state-of-the-art treatment for cardiovascular stenosis is an angioplasty in combination with stenting of the affected artery. Stents can be either laser cut out of a tube or an interwoven such as a braided structure. Furthermore, there are two groups of stents regarding their expansion behaviours: balloon expandable and self-expandable. Within this paper, a new approach to braiding stent-like structures out of a novel shape memory polymer fibre will be discussed. Furthermore, the heat treatment of the stent structure will be investigated to improve its characteristics such as radial stiffness.