The simulation technique and its applications to infinitary combinatorics under the axiom of Blackwell determinacy

Benedikt Löwe

Vol. 214 (2004), No. 2, 335–358

DOI: 10.2140/pjm.2004.214.335

Abstract

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 combinatorial consequences that can be seen as an important step towards proving Tony Martin’s conjecture.

Milestones

Received: 15 April 2003

Revised: 8 August 2003

Published: 1 April 2004