User:Lambiam/DraftRFC

This is a draft version of a possible RFC regarding the disposition of page Boolean algebra.

Request for comments: should Boolean algebra be a disambiguation page?

{{rfctag|sci}} Should Boolean algebra be a disambiguation page or an article, and if the latter, what should be its main topic?  --Lambiam ~~~~~

Statement of the dispute

The term "Boolean algebra" can be used in two closely related, but distinguishable senses:

• the term can refer to a specific calculus, which uses laws that resemble the laws of elementary algebra. This is the meaning as used in the following quotation: "George Boole was a mathematician whose algebra of logic, now called Boolean algebra, is basic to the design of digital circuits." Used in this sense, the term is a non-count noun;
• the term can refer to any of several algebraic structures. This is the meaning in: "The collection of clopen subsets of a topological space forms a Boolean algebra." Used in this sense, the term is a count noun: it is meaningful to ask how many Boolean algebras (distinct up to isomorphism) of some given nature exist.

The relation between the two is that a Boolean algebra (count noun) is any structure that is a model of Boolean algebra (non-count noun). Every (countable) Boolean algebra is (up to isomorphism) a Lindenbaum–Tarski algebra of a theory of propositional calculus, essentially meaning that any formula satisfied in the Boolean algebra with carrier {0, 1} is satisfied in any Boolean algebra.

Given that there are two meanings, both of which should be treated with sufficient depth, the question arises how to handle this. One approach is to let the page whose title is "Boolean algebra" be a disambiguation page, with two entries corresponding to the two meanings – while explaining how the two meanings relate. Another approach is to let that page be an article about the common elements of the two meanings, which are the operations and the laws. Yet another approach is to let the page Boolean algebra be primarily about one of the two meanings (although also treating the other meaning, but in less depth), with a hatnote referring the reader to the other kind of Boolean algebra, as follows:

This article is about <one meaning>. For <other meaning>, see Boolean algebra (...).

Our guideline on disambiguation pages states that the second approach is to be preferred if one sense can be considered the "primary topic", that is, the topic that is much more likely to be the subject being sought by a reader entering "Boolean algebra" in the Search box than the other topic.

A dispute has arisen on which of these situations applies most closely to the situation at hand; hence this request for input from a wider audience.  --Lambiam ~~~~~