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)

The task proves too daunting. I can't take it at the moment; the amount of detail to be filled in by the reader is extreme and the subjects discussed are incredibly diverse considered that they are all about BAs. It may well be better for me to return to the category theory department, or perhaps venture into model theory. I am nowadays naturally concerned with these matters as they form (the basis for) the subject of my MSc. thesis. I have been beaten by BAs - how embarrassing. --Lord_Farin (talk) 21:17, 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.