In this paper we classify finite special Moufang sets M(U, τ ) of odd characteristic. The characteristic 2 case was handled in another paper by De Medts and the author. We prove, using elementary means that U is elementary abelian. Then we show that M(U, τ ) is the unique Moufang set whose little projective group is PSL2(|U |). The emphasis of this paper is on obtaining elementary proofs. Secti...

Proof Theory is the branch of mathematical logic that investigates mathematical reasoning and mathematical proofs. This area emanated from Hilbert’s Program calling for consistency proofs of formal theories. In the 1950s the focus of proof theory began shifting towards applications of formal methods to concrete proofs in order to obtain new mathematical results. The method CERES (cut-eliminatio...

We study classes of minimal sets defined by restrictions on the possible extensions of the words. These sets generalize the previously studied classes of neutral and tree sets by relaxing the condition imposed on the empty word and measured by an integer called the characteristic of the set. We present several enumeration results holding in these sets of words. These formulae concern return wor...

A characteristic pair is a pair (G, C) of polynomial sets in which G is a reduced lexicographic Gröbner basis, C is the minimal triangular set contained in G, and C is normal. In this paper, we show that any finite polynomial set P can be decomposed algorithmically into finitely many characteristic pairs with associated zero relations, which provide representations for the zero set of P in term...