The Axiom of Blackwell Determinacy is a set-theoretic axiom motivated by games used in statistics. It is known that the Axiom of Determinacy implies the Axiom of Blackwell Determinacy. Tony Martin has conjectured that the two axioms are equivalent. We develop the “simulation technique” which allows us to simulate boundedness proofs under the assumption of Blackwell Determinacy and deduce strong...

The Pasch axiom is a strong geometric property which was noted and discussed even from the period of Euclid. Modern geometers followed the study of the Pasch axiom and in the context of axiomatic convexity this axiom was widely studied by pioneers in convexity theory. The connected graphs G for which the geodesic interval function I satisfies the Pasch axiom were characterized by Chepoi in 1994...

In this article we discuss some elementary concepts in axiomatics, which is the study of axioms. The axiomatic system we use is that of a metric space, which will be familiar to many readers. Metric spaces were introduced by the French mathematician Maurice Fréchet in 1906 as a generalization of the real numbers and the “distance function” f (x , y) = |x − y|. The aim is to construct limits, co...