User:Lord Farin/Long-Term Projects/Givant-Halmos

= Processing of 'Introduction to Boolean Algebras' =


 * : $\S 1$: Definition $1.1$


 * : $\S 1$: Definition $1.1$

First page it covers: Integer Addition is Associative.

First page covered by Appendices: Definition:Set.

A book dedicated to boolean algebras. BAs crop up so frequently that I deemed it inevitable to cover them without delay (having grinded to a halt on two other projects because of this void).

Progress thus far
Initial set-up complete. --Lord_Farin 20:10, 7 August 2012 (UTC)

Completed covering Appendix A. Continue with Chapter 1 (yay). --Lord_Farin (talk) 17:26, 14 December 2012 (UTC)

An evening-long dash brought us to $\S 1$, Exc. $7$; p.6. --Lord_Farin (talk) 23:13, 14 December 2012 (UTC)

Up to $\S 2$, p.8 (ended at Two-Valued Functions form Boolean Algebra). --Lord_Farin (talk) 19:24, 18 December 2012 (UTC)

Up to $\S 3$, p.14 (started at Definition:Characteristic Function/Set). --Lord_Farin (talk) 09:35, 23 January 2013 (UTC)

Missing Proofs

 * Group Operation is Cancellable

Skipped thus far (that is, what needs to be done still)

 * The proof of the Cantor-Bernstein-Schroeder Theorem given in Appendix A.
 * The genuinely hard exercises of $\S 1$
 * Some interesting characterizations of Boolean algebras in the exercises of $\S 2$

Other things

 * Definition:Two (Ring) can be dealt with more elementarily; this brings also the need for some theorems, which need apt references from Halmos-Givant.
 * Patch up the area around Definition:Boolean-Valued Function which is a mess.
 * Category:Idempotent Rings to be created and populated.