Daisuke Ikegami, David de Kloet, Benedikt Löwe
The Axiom of Real Blackwell Determinacy
Preprint series: ESI preprints

MSC:

03E60 Determinacy and related principles which contradict the axiom of choice

03E15 Descriptive set theory, See also {04A15, 28A05, 54H05}

03E35 Consistency and independence results

90D05 $2$-person games

90D44 Games involving topology or set theory

Abstract: The theory of infinite games with slightly imperfect information has been focusing on games with finitely and
countably many moves. In this paper, we shift the discussion to games with uncountably many possible moves,
introducing the axiom of real Blackwell determinacy $\BlAD_\R$ (as an analogue of the axiom of real
determinacy $\AD_\R$). We prove that the consistency strength of $\BlAD_\R$ is strictly greater than
that of $\AD$.


Keywords: real Blackwell determinacy, sharps, consistency strength, real determinacy, axiom of choice