# SUPPLEMENTARY TEXT

The items on this web page augment the book

### Logic for Mathematics and Computer Science.

This text is referred to simply as LMCS in the following.
Theorem 10.16 of Chapter II would be identified as Theorem II.10.16 of LMCS.

Footnotes in the HTML files are handled by the icon .
Clicking on the icon will take one to a separate page with the footnote.

Some of the following items are marked with an asterisk (*).
This indicates that one probably needs more background than LMCS provides.
For speedy downloading and printout it is better to use the .pdf (for PC's) or the .dvi or .ps versions (if you have a UNIX workstation).

Chapter I: From Aristotle to Boole

•  A proof of Boole's Expansion Theorem (.pdf file) (.dvi file) (.ps file)

•  A proof of Boole's Elimination Theorem (.pdf file) (.dvi file) (.ps file)

Chapter II: Propositional Logic

§7 Valid arguments

•  Comparing the expressive power of propositional logic to that of the calculus of classes (.pdf file) (.dvi file) (.ps file)

•  Comments on Boolean algebra (.pdf file) (.dvi file) (.ps file)

§8 Compactness

•  A second proof of compactness, using binary trees (.pdf file) (.ps file)

§9 The Propositional Proof System PC

•  An algorithm to find derivations in PC (.pdf file) (.ps file)

•  General discussion of propositional proof systems (.pdf file) (.dvi file) (.ps file)

•  (*) The relative strength of propositional proof systems (.pdf file) (.ps file)

Chapter III: Equational Logic

•  (*) Quasi-identity logic (.pdf file) (.dvi file) (.ps file)

Chapter IV: Predicate Clause Logic

Chapter V: First-Order Logic

Chapter VI: A Proof System for First-Order Logic, and Gödel's Completeness Theorem

• The Logicians I. Whately, De Morgan, Boole, Jevons

 Numbers, Sets and Mathematical Logic: The Logicians II. [ single PS file - 400K ] [ single PDF file 500K ]

This consists of comments on the work in logic from:

• An earlier version of the notes on Cantor quoted correspondence from Dedekind to Cantor. The correspondence was actually from Cantor to Dedekind. This has been corrected in the current version. (March 13, 2001)

•  The Principia Mathematica of Whitehead and Russell (.pdf file) (.dvi file) (.ps file)