## Expository Papers - R. G. Swan

**Tarski's Principle and the Elimination of Quantifiers**(pdf)
- This is an expository article on Tarski's principle and the elimination
- of quantifiers for real closed and algebraically closed fields.

**van der Waerden's Theorem on Arithmetic Progressions**(pdf)
- We give a simplified version of a proof of van der Waerden's
- theorem that if a sufficiently long interval of integers is
- partitioned into a specified number of parts, one will contain
- an arithmetic progression of given length.

**The Morse Sequence**(pdf)
- We give a proof that the Morse sequence has no 3 times repeated block
- and derive from it a sequence on 3 letters that has no repeated block.

**Goldie's Theorem**(pdf)
- This is an exposition of Goldie's theorem with a section on Ore localization
- and with an application to defining ranks for finitely generated modules
- over non--commutative noetherian rings.

**The Flabby Class Group of a Finite Cyclic Group**(pdf)
- This is an expository paper on work of Endo and Miyata which leads
- to a computation of the flabby class group of a finite cyclic group.