Independence and consistency proofs in quadratic form theory

Variational Theory: Variable-independence and Consistency

VARIATIONAL THEORY: VARIABLE-INDEPENDENCE AND CONSISTENCY Jian-zhong Zhao Geophysics Department, College of Resource, Environment and Earth Sciences, Yunnan University, Kunming, P.R. China 650091 [email protected] Abstract Variational theory of elasticity is surveyed in the context of mathematical logic in the present paper. The problem of variable-independence of variational principles ra...

SET THEORY An Introduction to Independence Proofs

Propositional Consistency Proofs

Partial consistency statements can be expressed as polynomial-size propositional formulas. Frege proof systems have polynomial-size partial self-consistency proofs. Frege proof systems have polynomialsize proofs of partial consistency of extended Frege proof systems if and only if Frege proof systems polynomially simulate extended Frege proof systems. We give a new proof of Reckhow’s theorem th...

Direct Proofs of Order Independence

We establish a generic result concerning order independence of a dominance relation on finite games. It allows us to draw conclusions about order independence of various dominance relations in a direct and simple way.

The Elementary Type Conjecture in Quadratic Form Theory

The systematic study of quadratic forms over an arbitrary field of characteristic = 2 was initiated by Witt [W]. Two milestone papers in the area are a paper of Pfister [P0] relating quadratic forms and orderings and the paper of Milnor [M] pointing out a possible relationship between the Witt ring of quadratic forms and the Galois cohomology of the field (a relationship eventually verified by ...