An infinity which depends on the axiom of choice
نویسندگان
چکیده
منابع مشابه
An infinity which depends on the axiom of choice
In the early years of set theory, Du Bois Reymond introduced a vague notion of infinitary pantachie meant to symbolize an infinity bigger than the infinity of real numbers. Hausdorff reformulated this concept rigorously as a maximal chain (a linearly ordered subset) in a partially ordered set of certain type, for instance, the set N N under eventual domination. Hausdorff proved the existence of...
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Hilbert’s machine is a supertask machine inspired by Hilbert’s Hotel whose functioning leads to a contradiction that compromises the Axiom of Infinity. 1. Hilbert’s Machine In the following conceptual discussion we will make use of a theoretical device that will be referred to as Hilbert’s machine, composed of the following elements (see Figure 1): (1) An infinite tape similar to those of Turin...
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Let 6 e be an elementary topos. The axiom of infinity, asserting that 5 e has a natural numbers object, is shown to be necessary-sufficiency has long been k n o w n f o r the existence of an object-classifying topos over 5 e. In the known constructions [1, 4, 6] of classifying topoi for geometric theories, it is always assumed that the base topos fie satisfies the axiom of infinity. The purpose...
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ژورنال
عنوان ژورنال: Applied Mathematics and Computation
سال: 2012
ISSN: 0096-3003
DOI: 10.1016/j.amc.2011.05.003