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 appears to be little amenable to computational interpretation. This received view, however, ...
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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...
Your privacy, your choice We use essential cookies to make sure the site can function. We also use optional cookies for advertising, personalisation of content, usage analysis, and social media. By accepting optional cookies, you consent to the processing of your personal data - including ...
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...
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. ...
2.2 Characterizing distributed computations Distributed configurations conforming to CMbasic can be characterized by a rewrite rule (4) and an axiom (t). Rule (4) is the conditional rewrite rule given below: <)(w, N, w', N', !1) w II N -+ w' II N' II !1 Rule (4) defines the...
{M}_i\). We stress that displacements and their derivatives are different such that the energy density is different in each position. Nevertheless, for the whole body, the total energy is equivalent at both scales. This assertion is the key axiom in nearly all homogenization theories based on...
Axiom 1 IfSis a connected component ofg, then the members of the coalitionSought to allocate to themselves the total valuev(S) available to them, i.e.,\(\forall S\in N|g\), $$\begin{aligned} \sum _{i\in S} Y_i(v, g)=v\left( S\right) . \end{aligned}$$ ...