Sentence examples for dependent choices from inspiring English sources

In fact, N Brunner [18] has shown that any proof of (E) requires at least the basic axioms of Zermelo-Fraenkel (ZF) plus a form of the Axiom of Choice called the Axiom of Dependent Choices (DC), whereas R Mańka has shown in [19] that (C) holds wholly within (ZF).

These approaches have led to valuable insights in optimal responses, state dependent choices, and behavioural strategies in social contexts.

The Axiom of Dependent Choices (DC) may be formulated precisely as follows.

The Axiom of Dependent Choices (DC), sometimes called the 'Axiom of inductive definition of sequences',11 appears to be essential for the development of the foundations of functional analysis at least in the separable case (see, for example, the discussions in [20, 21]).

For an arbitrary doubly-indexed family of sets \(\{M_{i,j}: i \in I,j \in J\}\), and where \(J^I\) is the set of all functions with domain \(I\) and which take values in \(J\): A much-studied special case of AC is the Principle of Dependent Choices (Bernays 1942, Tarski 1948).

It also has a restricted form of the axiom of dependent choice.

For example one could add the principle of countable choice (AC0) or that of dependent choice (DC).

Since the axiom of dependent choice is consistent with an important axiom in classical set theory (the axiom of determinacy) while the full axiom of choice is not, special attention is payed to this axiom and in general one tries to reduce the amount of choice in a proof, if choice is present at all, to dependent choice.

The calculated binding energy scores from the docking procedure are used to obtain the statistical weights for the pair wise dependent choice of amino acids.

The dependent choice variable was binary-coded as 0 or 1 (1 = chosen; 0 = not chosen).

Stocking-rate decisions appear to be slow, path-dependent choices that are shaped by broader social, economic, and political dynamics.