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 | |
| Publication status | Published - 2012 Oct 1 |
| Externally published | Yes |
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Keywords
- Blackwell games
- Consistency strength
- Real determinacy
- Sharps
ASJC Scopus subject areas
- Logic
- Philosophy
Cite this
The axiom of real Blackwell determinacy. / Ikegami, Daisuke; de Kloet, David; Löwe, Benedikt.
In: Archive for Mathematical Logic, Vol. 51, No. 7-8, 01.10.2012, p. 671-685.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - The axiom of real Blackwell determinacy
AU - Ikegami, Daisuke
AU - de Kloet, David
AU - Löwe, Benedikt
PY - 2012/10/1
Y1 - 2012/10/1
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
UR - http://www.scopus.com/inward/record.url?scp=84867098588&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84867098588&partnerID=8YFLogxK
U2 - 10.1007/s00153-012-0291-x
DO - 10.1007/s00153-012-0291-x
M3 - Article
AN - SCOPUS:84867098588
VL - 51
SP - 671
EP - 685
JO - Archive for Mathematical Logic
JF - Archive for Mathematical Logic
SN - 0933-5846
IS - 7-8
ER -