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Review: W. Hugh Woodin, The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal
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The axiom of determinacy and the prewellordering property
Lecture Notes in Mathematics, 1981Let ω = (0,1,2,.) be the set of natural numbers and R = ω^ω the set of all functions from ω into ω, or for simplicity reals. A product space is of the form X = X_1 x X_2 x . x X_k, where X_1 = ω or R. Subsets of these product spaces are called pointsets.
Kechris, Alexander S. +2 more
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The axiom of determinacy, strong partition properties and nonsingular measures
Lecture Notes in Mathematics, 1981In this paper we study the relationship between AD and strong partition properties of cardinals as well as some consequences of these properties themselves. ; © 1981 Springer. Research partially supported by NSF Grant MCS79-20465. The author is an A. P. Sloan Foundation Fellow. Research partially supported by NSF Grant MCS78-03744.
Kechris, Alexander S. +3 more
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The axiom of determinacy and the modern development of descriptive set theory
Journal of Soviet Mathematics, 1988Translation from Itogi Nauki Tekh., Ser. Algebra, Topologiya, Geom. 23, 3-50 (1985; Zbl 0625.03030).
Vladimir Kanovei
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Axioms of determinacy and biorthogonal systems
Israel Journal of Mathematics, 1989Let X be a norm-closed and not norm-separable subspace of \(\ell^{\infty}({\mathbb{N}})\). The authors study the question of whether X contains a biorthogonal system of cardinality \(2^{\aleph_ 0}\). The answer depends on the set theory which is used. For example, if X is in the projective hierarchy with respect to the \(w^*\)-topology [i.e.
Godefroy, Gilles, Louveau, Alain
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Some Axioms of Weak Determinacy
2009We consider two-player games of perfect information of length some cardinal $\kappa$. It is well-known that for $\kappa \geq \omega_1$ the full axiom of determinacy for these games fails, thus we investigate three weaker forms of it. We obtain the measurability of $\kappa^{+}$ under $DC_{\kappa}$-the axiom of dependent choices generalized to $\kappa ...
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The Destruction of the Axiom of Determinacy by Forcings on $\mathbb{R}$ when $��$ is Regular
2019$\mathsf{ZF + AD}$ proves that for all nontrivial forcings $\mathbb{P}$ on a wellorderable set of cardinality less than $ $, $1_{\mathbb{P}} \Vdash_{\mathbb{P}} \neg\mathsf{AD}$. $\mathsf{ZF + AD} + $ is regular proves that for all nontrivial forcing $\mathbb{P}$ which is a surjective image of $\mathbb{R}$, $1_{\mathbb{P}} \Vdash_{\mathbb{P}} \neg ...
Chan, William, Jackson, Stephen
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Partition Properties for Non-Ordinal Sets under the Axiom of Determinacy
In this paper we explore coloring theorems for the reals, its quotients, cardinals, and their combinations. This work is done under the scope of the axiom of determinacy. We also explore generalizations of Mycielski's theorem and show how these can be used to establish coloring theorems. To finish, we discuss the strange realm of long unions.openaire +2 more sources