Template:BPI

Template
Include this template at (or near) the bottom of any page which depends, either directly or indirectly, on the Boolean Prime Ideal Theorem.

Usage
This template can be invoked as:



or:



where  is the ProofWiki page name of a proof which itself depends on BPI.

If you want this to apply to just one of the proofs of a given theorem, then there exists an optional second 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 Boolean Prime Ideal Theorem category, and the following being added to the page:

Boolean Prime Ideal Theorem
This theorem depends on the Boolean Prime Ideal Theorem (BPI), by way of (link to proof name).

Although not as strong as the Axiom of Choice, the BPI 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.

This depends on the Boolean Prime Ideal Theorem (BPI).

Although not as strong as the Axiom of Choice, the BPI 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.