Computational contentConstructive set theoryFinite binary treeInductive generationAs a fairly frequent form of the Axiom of Choice about relatively simple structures (posets), Hausdorff's Maximal Chain Principle
Contemporary theoretical physics postulates at least three types of randomness: (i) the “chaotic” randomness residing in the initial conditions, which are assumed to be “drawn” (via the postulated axiom of choice) from a “continuum urn.” Almost all elements of the continuum are nonrecursive...
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Luce, R. D. (1977). The choice axiom after twenty years.Journal of Mathematical Psychology,15(3), 215–233. ArticleGoogle Scholar Malt, B. C., & Smith, E. E. (1984). Correlated properties in natural categories.Journal of Verbal Learning and Verbal Behavior,23(2), 250–269. ...
This paper exposes a contradiction in the Zermelo-Fraenkel set theory with the axiom of choice (ZFC). While Godel's incompleteness theorems state that a consistent system cannot prove its consistency, they do not eliminate proofs using a stronger system or methods that are outside the scope of...
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(see remark 1.1 ). let us here summarize our main results. we present axiom systems for covectors of affine oriented matroids (aoms) over arbitrary ground sets (sect. 2 ). these support canonical operations such as reorientation and taking minors (sect. 2.1 ). in particular our ...
We present a logical framework that enables us to define a formal theory of computational trust in which this notion is analysed in terms of epistemic atti
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