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Determinacy and the tree property
, 2003
"... The following theorems are shown. (A) If ω2 and ω3 have the tree property and either 2 ℵ0 = ℵ2 or Ω is measurable then Π 1 2 Determinacy holds. (B) If ωn has the tree property for all n < ω, n ≥ 2, and 2 <ℵω = ℵω then Projective Determinacy holds. 1 Introduction. A cardinal δ is said to have t ..."
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The following theorems are shown. (A) If ω2 and ω3 have the tree property and either 2 ℵ0 = ℵ2 or Ω is measurable then Π 1 2 Determinacy holds. (B) If ωn has the tree property for all n < ω, n ≥ 2, and 2 <ℵω = ℵω then Projective Determinacy holds. 1 Introduction. A cardinal δ is said to have
Large Cardinals and Determinacy
, 2011
"... The developments of set theory in 1960’s led to an era of independence in which many of the central questions were shown to be unresolvable on the basis of the standard system of mathematics, ZFC. This is true of statements from areas as diverse as analysis (“Are all projective sets Lebesgue measura ..."
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The developments of set theory in 1960’s led to an era of independence in which many of the central questions were shown to be unresolvable on the basis of the standard system of mathematics, ZFC. This is true of statements from areas as diverse as analysis (“Are all projective sets Lebesgue
Determinacy of a Rational Moment Problem
, 1999
"... We discuss a moment problem of Stieltjes type that is related to the theory of orthogonal rational functions. We obtain results which lead to a suÆcient condition of Carleman type for determinacy of the moment problem. Key words: rational moment problem, orthogonal rational functions AMS Subject cl ..."
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We discuss a moment problem of Stieltjes type that is related to the theory of orthogonal rational functions. We obtain results which lead to a suÆcient condition of Carleman type for determinacy of the moment problem. Key words: rational moment problem, orthogonal rational functions AMS Subject
Generalised projections in finite state automata and decidability of state determinacy
, 2008
"... Loss of sensors and communication links may lead to incomplete observation at the supervisory level of discrete event systems (DES). Under these circumstances, an event may conceivably be observable at one state and unobservable at another state and the observability may become dependent on the hist ..."
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on the history of event occurrences. This paper presents a framework for analysis of generalised projection maps in DES, including the maps that introduce possibly unbounded memory
Cardinals as Ultrapowers A Canonical Measure Analysis under the Axiom of Determinacy
"... My interest in logic and set theory was first raised when I realized that mathematics is not just about calculations with numbers but about formal systems, about the consequences that follow from applying specific rules to formal statements, so that the whole of mathematics can be concluded from axi ..."
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cardinals and determinacy. My Master’s thesis was about supercompact cardinals under the Axiom of Determinacy and would not have happened without the support of Benedikt Löwe. I started my PhD studies in Bonn under the supervision of Benedikt Löwe who soon after moved to Amsterdam. In Bonn, I was first a
Forthcoming in Philosophical Psychology Representationalism and the Determinacy of Visual Content
"... Abstract DETERMINACY is the claim that covert shifts in visual attention sometimes affect the determinacy of visual content. (Capital letters will distinguish the claim from the familiar word, “determinacy.”) Representationalism is the claim that visual phenomenology supervenes on visual representa ..."
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Abstract DETERMINACY is the claim that covert shifts in visual attention sometimes affect the determinacy of visual content. (Capital letters will distinguish the claim from the familiar word, “determinacy.”) Representationalism
BOUNDED MARTIN’S MAXIMUM WITH MANY WITNESSES
, 2008
"... We study a strengthening of Bounded Martin’s Maximum which asserts that if a Σ1 fact holds of ωV 2 in a stationary set preserving extension then it holds in V for a stationary set of ordinals less than ω2. We show that this principle implies Global Projective Determinacy, and therefore does not ho ..."
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We study a strengthening of Bounded Martin’s Maximum which asserts that if a Σ1 fact holds of ωV 2 in a stationary set preserving extension then it holds in V for a stationary set of ordinals less than ω2. We show that this principle implies Global Projective Determinacy, and therefore does
Weakly Ramsey sets in Banach Spaces
, 2000
"... Abstract. We give a sucient condition for a set of block subspaces in an in nitedimensional Banach space to be weakly Ramsey. Using this condition we prove that in the Levycollapse of a Mahlo cardinal, every projective set is weakly Ramsey. This, together with a construction of W. H. Woodin, is us ..."
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Cited by 15 (1 self)
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, is used to show that the Axiom of Projective Determinacy implies that every projective set is weakly Ramsey. In the case of c0 we prove similar results for a stronger Ramsey property. And for hereditarily indecomposable spaces we show that the Axiom of Determinacy plus the Axiom of Dependent Choices imply
{TANDF_FPP}TCON/TCON_A_289050.3d (TCON) [First Proof] International Journal of Control Vol.??, No.?, Month?? 2008, 1–19 Generalised projections in finite state automata and decidability of state determinacy
, 2007
"... Loss of sensors and communication links may lead to incomplete observation at the supervisory level of discrete event systems (DES). Under these circumstances, an event may conceivably be observable at one state and 10 unobservable at another state and the observability may become dependent on the h ..."
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on the history of event occurrences. This paper presents a framework for analysis of generalised projection maps in DES, including the maps that introduce possibly unbounded memory
THE STRENGTH OF PROJECTIVE MARTIN CONJECTURE
"... Abstract. We show that Martin’s conjecture on Π11functions uniformly ≤Torder preserving on a cone implies Π11 Turing Determinacy over ZF+DC. In addition, it is also proved that for n ≥ 0, this conjecture for uniformly degree invariant Π12n+1functions is equivalent over ZFC to Σ12n+2Axiom of Dete ..."
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Abstract. We show that Martin’s conjecture on Π11functions uniformly ≤Torder preserving on a cone implies Π11 Turing Determinacy over ZF+DC. In addition, it is also proved that for n ≥ 0, this conjecture for uniformly degree invariant Π12n+1functions is equivalent over ZFC to Σ12n+2Axiom
Results 1  10
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32