The axiom of real Blackwell determinacy

Daisuke Ikegami; David de Kloet; Benedikt Löwe

doi:10.1007/s00153-012-0291-x

The axiom of real Blackwell determinacy

Daisuke Ikegami, David de Kloet, Benedikt Löwe

Research output: Contribution to journal › Article › peer-review

Abstract

The theory of infinite games with slightly imperfect information has been developed for 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 Bl-AD _ℝ (as an analogue of the axiom of real determinacy AD _ℝ). We prove that the consistency strength of Bl-AD _ℝ is strictly greater than that of AD.

Original language	English
Pages (from-to)	671-685
Number of pages	15
Journal	Archive for Mathematical Logic
Volume	51
Issue number	7-8
DOIs	https://doi.org/10.1007/s00153-012-0291-x
Publication status	Published - 2012 Oct
Externally published	Yes

Keywords

Blackwell games
Consistency strength
Real determinacy
Sharps

ASJC Scopus subject areas

Philosophy
Logic

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AU - Löwe, Benedikt

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N2 - The theory of infinite games with slightly imperfect information has been developed for 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 Bl-AD ℝ (as an analogue of the axiom of real determinacy AD ℝ). We prove that the consistency strength of Bl-AD ℝ is strictly greater than that of AD.

AB - The theory of infinite games with slightly imperfect information has been developed for 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 Bl-AD ℝ (as an analogue of the axiom of real determinacy AD ℝ). We prove that the consistency strength of Bl-AD ℝ is strictly greater than that of AD.

KW - Blackwell games

KW - Consistency strength

KW - Real determinacy

KW - Sharps

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The axiom of real Blackwell determinacy

Abstract

Keywords

ASJC Scopus subject areas

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