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12
A hierarchy of Deterministic Contextfree ωlanguages
"... Twenty years ago, Klaus. W. Wagner came up with a hierarchy of ωregular sets that actually bears his name. It turned out to be exactly the Wadge hierarchy of the sets of ωwords recognized by Deterministic Finite Automata. We describe the Wadge hierarchy of contextfree ωlanguages, which stands as ..."
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Cited by 11 (5 self)
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Twenty years ago, Klaus. W. Wagner came up with a hierarchy of ωregular sets that actually bears his name. It turned out to be exactly the Wadge hierarchy of the sets of ωwords recognized by Deterministic Finite Automata. We describe the Wadge hierarchy of contextfree ωlanguages, which stands as an extension of Wagner's work from Automata to Pushdown Automata.
The core model for almost linear iterations
 Annals of Pure and Appl. Logic 116 (2002
"... We introduce 0 • (“zero handgrenade”) as a sharp for an inner model with a proper class of strong cardinals. We prove the existence of the core model K in the theory “ZFC + 0 • doesn’t exist. ” Combined with work of Woodin, Steel, and earlier work of the author, this provides the last step for de ..."
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Cited by 7 (4 self)
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We introduce 0 • (“zero handgrenade”) as a sharp for an inner model with a proper class of strong cardinals. We prove the existence of the core model K in the theory “ZFC + 0 • doesn’t exist. ” Combined with work of Woodin, Steel, and earlier work of the author, this provides the last step for determining the exact consistency strength of the assumption in the statement of the 12th Delfino problem (cf. [12]). 0 Introduction. Core models were constructed in the papers [2], [13], [7], [15] and [16], [8] (see also [23]), [27], and [28]. We refer the reader to [6], [17], and [14] for less painful introductions into core model theory. A core model is intended to be an inner model of set theory (that is, a transitive
Classical And Constructive Hierarchies In Extended Intuitionistic Analysis
"... This paper introduces an extension of Kleene's axiomatization of Brouwer's intuitionistic analysis, in which the classical arithmetical and analytical hierarchies are faithfully represented as hierarchies of the domains of continuity. A domain of continuity is a relation R(#) on Baire space with t ..."
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Cited by 4 (3 self)
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This paper introduces an extension of Kleene's axiomatization of Brouwer's intuitionistic analysis, in which the classical arithmetical and analytical hierarchies are faithfully represented as hierarchies of the domains of continuity. A domain of continuity is a relation R(#) on Baire space with the property that every constructive partial functional defined on {# : R(#)} is continuous there. The domains of continuity for coincide with the stable relations (those equivalent in to their double negations), while every relation R(#) is equivalent in #) for some stable A(#, #) (which belongs to the classical analytical hierarchy). The logic of is intuitionistic. The axioms of include countable comprehension, bar induction, Troelstra's generalized continuous choice, primitive recursive Markov's Principle and a classical axiom of dependent choices proposed by Krauss. Constructive dependent choices, and constructive and classical countable choice, are theorems.
Guarded Quantification in Least Fixed Point Logic
, 2002
"... We develop a variant of Least Fixed Point logic based on First Order logic with a relaxed version of guarded quantification. We develop a Game Theoretic Semantics of this logic, and find that under reasonable conditions, guarding quantification does not reduce the expressibility of Least Fixed Point ..."
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Cited by 2 (1 self)
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We develop a variant of Least Fixed Point logic based on First Order logic with a relaxed version of guarded quantification. We develop a Game Theoretic Semantics of this logic, and find that under reasonable conditions, guarding quantification does not reduce the expressibility of Least Fixed Point logic. But guarding quantification increases worstcase time complexity.
Countable homogeneous and partially homogeneous ordered structures
"... I survey classification results for countable homogeneous or `partially homogeneous' ordered structures. This includes some account of Schmerl's classification of the countable homogeneous partial orders, outlining an extension of this to the coloured case, and also treating results on linear order ..."
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Cited by 2 (1 self)
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I survey classification results for countable homogeneous or `partially homogeneous' ordered structures. This includes some account of Schmerl's classification of the countable homogeneous partial orders, outlining an extension of this to the coloured case, and also treating results on linear orders, and their generalizations, trees and cyclefree partial orders.
Cardinalities in the projective hierarchy
"... 1 Introduction We show that the "effective cardinality " of the collection of \Pi,1n+1 sets is strictly bigger than the effective cardinality of the \Pi,1n. The phrase effective cardinality is vague but can be made exact in the usual ways. For instance: ..."
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1 Introduction We show that the "effective cardinality " of the collection of \Pi,1n+1 sets is strictly bigger than the effective cardinality of the \Pi,1n. The phrase effective cardinality is vague but can be made exact in the usual ways. For instance:
Delays, Recurrence and Ordinals
 Proc. London Math. Soc
"... Let X be a Polish spaceÐthat is, a complete, separable metric spaceÐand let f: X! X be a continuous function. We write q for the set of natural numbers f0; 1; 2;...g, and for k 2 q, f k for the kth iterate of f, so that for each x 2 X, f 0 …x † ˆx and f k ‡ 1 …x † ˆf … f k …x††. Forxand y in X we de ..."
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Cited by 1 (1 self)
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Let X be a Polish spaceÐthat is, a complete, separable metric spaceÐand let f: X! X be a continuous function. We write q for the set of natural numbers f0; 1; 2;...g, and for k 2 q, f k for the kth iterate of f, so that for each x 2 X, f 0 …x † ˆx and f k ‡ 1 …x † ˆf … f k …x††. Forxand y in X we de®ne
Game Representations of Complexity Classes
 Proc. Eur. Summer School on Logic, Language and Information (European Assoc. Logic, Language and Information
, 2001
"... Many descriptive and computational complexity classes have gametheoretic representations. These can be used to study the relation between different logics and complexity classes in finite model theory. ..."
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Many descriptive and computational complexity classes have gametheoretic representations. These can be used to study the relation between different logics and complexity classes in finite model theory.
Strong Statements of Analysis
 Bulletin of the London Mathematical Society
"... Examples are discussed of natural statements about irrational numbers that are equivalent, provably in ZFC, to strong settheoretical hypotheses, and of apparently classical statements provable in ZFC of which the only known proofs use strong settheoretical concepts. 1. ..."
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Examples are discussed of natural statements about irrational numbers that are equivalent, provably in ZFC, to strong settheoretical hypotheses, and of apparently classical statements provable in ZFC of which the only known proofs use strong settheoretical concepts. 1.