Results 21 to 30 of about 3,584 (122)
, 1996 Blackwell games are infinite games of imperfect information. The two players simultaneously make their moves, and are then informed of each other's moves.
Vervoort, Marco R.
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Ideals and strong axioms of determinacy
Journal of the American Mathematical SocietyWe show that the following two theories are equiconsistent: (T) ZFC, CH and "There is a dense ideal on the first uncountable cardinal such that if j is the generic embedding associated with it then its restriction on ordinals is independent of the generic object is". (S) ZF, ADR and "Theta is a regular cardinal." The main result of this paper is that T
Dominik Adolf +4 more
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How unprovable is Rabin's decidability theorem?
, 2015 We study the strength of set-theoretic axioms needed to prove Rabin's theorem on the decidability of the MSO theory of the infinite binary tree. We first show that the complementation theorem for tree automata, which forms the technical core of typical ...
Beckmann A. +6 more
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, 2016 In this commemorative article, the work of Richard Laver is surveyed in its full range and extent.Accepted ...
Kanamori, Akihiro
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Consequences of the Axiom of Blackwell Determinacy
Irish Mathematical Society Bulletin, 2002 This paper is both a survey and a research announcement. The author considers a class of two-person games with ``slightly imperfect'' information called Blackwell games. These games belong to the broader class of stochastic games. Two-person games with perfect information have played an important role in set theory via the Axiom of Determinacy (AD ...
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Determinacy on the edge of second‐order arithmetic, I
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract This is the first of two articles on the strength of m$m{}$‐Σ30$\bm{\Sigma }^0_3{}$‐determinacy for m∈N$m\in \mathbb {N}$, the strongest theories of determinacy contained in Hilbert's second‐order arithmetic (Z2)$(Z_2)$. In this article, we refute two natural conjectures on the strength of these principles in terms of inductive definability ...
J. P. Aguilera, P. D. Welch
wiley +1 more source
Coding and anticoding of a cardinal by bounded subsets of the cardinal
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract This paper will consider combinatorial properties related to coding a cardinal by its bounded subsets. These properties have traditionally been studied in the context of very large cardinals and variations of these properties either reach the level of Kunen inconsistency or are very close to it.
William Chan
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The Destruction of the Axiom of Determinacy by Forcings on $\mathbb{R}$ when $\Theta$ is Regular
Israel Journal of Mathematics, 2019 $\mathsf{ZF + AD}$ proves that for all nontrivial forcings $\mathbb{P}$ on a wellorderable set of cardinality less than $\Theta$, $1_{\mathbb{P}} \Vdash_{\mathbb{P}} \neg\mathsf{AD}$. $\mathsf{ZF + AD} + \Theta$ is regular proves that for all nontrivial forcing $\mathbb{P}$ which is a surjective image of $\mathbb{R}$, $1_{\mathbb{P}} \Vdash_{\mathbb{P}}
Chan, William, Jackson, Stephen
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Large cardinals and continuity of coordinate functionals of filter bases in Banach spaces
, 2020 Assuming the existence of certain large cardinal numbers, we prove that for every projective filter $\mathscr F$ over the set of natural numbers, $\mathscr{F}$-bases in Banach spaces have continuous coordinate functionals.
Kania, Tomasz, Swaczyna, Jarosław
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Purely Instrumental Agents Are Possible
Philosophy and Phenomenological Research, Volume 112, Issue 1, Page 88-101, January 2026.ABSTRACT Purely instrumental agents can reason about how to realize their ends, but not about which ends to pursue. They can do one thing in order to do another but cannot choose their final ends for reasons. Some have argued that such agents are impossible, and that the success of moral constitutivism depends on their impossibility.
Bennett Eckert‐Kuang
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