Template:Choice-principle

Template
Include this template at (or near) the bottom of any page which depends, either directly or indirectly, on a choice axiom that does not have its own specialized template. That is, a choice axiom not known to be equivalent in Zermelo-Fraenkel set theory to any of the following:


 * Axiom of Choice
 * Axiom of Dependent Choice
 * Axiom of Countable Choice
 * Axiom of Choice for Finite Sets
 * Boolean Prime Ideal Theorem

Examples of such choice principles include Order-Extension Principle, Ordering Principle, Axiom of Countable Choice for Finite Sets, and Hall's Marriage Theorem for general sets.

Usage
This template can be invoked as:



or:



where  is the  page name of a proof which itself depends on the named choice principle.

If you want this to apply to just one of the proofs of a given theorem, then there exists an optional third parameter which is a number (usually 3 or 4) determining the level of heading that the text of this template appears at. The default is 2 (standard heading) when the template itself is used so as to apply to the entire page.

Note: The current implementation is that only level 4 is available in this context.

Inclusion of this template will result in the page being added to the Choice Principles category, and the following being added to the page:

Choice Principle
This theorem depends on a choice principle, by way of (link to proof name).

Although not as strong as the Axiom of Choice, this choice principle is similarly independent of the Zermelo-Fraenkel axioms.

As such, most mathematicians are convinced of its truth and believe that it should be generally accepted.

This depends on.

Although not as strong as the Axiom of Choice, is similarly independent of the Zermelo-Fraenkel axioms.

As such, mathematicians are generally convinced of its truth and believe that it should be generally accepted.