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3,154
Stable Distributions, Pseudorandom Generators, Embeddings and Data Stream Computation
, 2000
"... In this paper we show several results obtained by combining the use of stable distributions with pseudorandom generators for bounded space. In particular: ffl we show how to maintain (using only O(log n=ffl 2 ) words of storage) a sketch C(p) of a point p 2 l n 1 under dynamic updates of its coo ..."
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Cited by 325 (15 self)
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(n) is much smaller than n; to our knowledge this is the first dimensionality reduction lemma for l 1 norm ffl we give an explicit embedding of l n 2 into l n O(log n) 1 with distortion (1 + 1=n \Theta(1) ) and a nonconstructive embedding of l n 2 into l O(n) 1 with distortion (1 + ffl
NonConstructive Computational Mathematics
 Journal of Automated Reasoning
, 1995
"... We describe a nonconstructive extension to Primitive Recursive Arithmetic, both abstractly, and as implemented on the BoyerMoore prover. Abstractly, this extension is obtained by adding the unbounded ¯ operator applied to primitive recursive functions; doing so, one can define the Ackermann functi ..."
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Cited by 2 (0 self)
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We describe a nonconstructive extension to Primitive Recursive Arithmetic, both abstractly, and as implemented on the BoyerMoore prover. Abstractly, this extension is obtained by adding the unbounded ¯ operator applied to primitive recursive functions; doing so, one can define the Ackermann
Nonconstructive aspects of topology
, 2008
"... Notes and slides will materialise at www.math.uu.se/˜palmgren ..."
Nonconstructible complexes and the bridge index
, 1999
"... We show that if a 3dimensional polytopal complex has a knot in its 1skeleton, where the bridge index of the knot is larger than the number of edges of the knot, then the complex is not constructible, and hence, not shellable. As an application we settle a conjecture of Hetyei concerning the shella ..."
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Cited by 13 (2 self)
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We show that if a 3dimensional polytopal complex has a knot in its 1skeleton, where the bridge index of the knot is larger than the number of edges of the knot, then the complex is not constructible, and hence, not shellable. As an application we settle a conjecture of Hetyei concerning the shellability of cubical barycentric subdivisions of 3spheres. We also obtain similar bounds concluding that a 3sphere or 3ball is nonshellable or not vertex decomposable. These two last bounds are sharp.
HINGES AND AUTOMORPHISMS OF THE DEGREES OF NONCONSTRUCTIBILITY
"... The main result of this paper is to show that, under weak cardinal assumptions, there is no nontrivial automorphism of the degrees of nonconstructibility. To achieve this we introduce the notion of a hinge. The degrees of nonconstructibility, or cdegrees, are the factor classes of the reals (in ..."
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The main result of this paper is to show that, under weak cardinal assumptions, there is no nontrivial automorphism of the degrees of nonconstructibility. To achieve this we introduce the notion of a hinge. The degrees of nonconstructibility, or cdegrees, are the factor classes of the reals (in
NONCONSTRUCTIVE PROPERTIES OF THE REAL NUMBERS
, 2000
"... Abstract. We study the relationship between various properties of the real numbers and weak choice principles. 1. Introduction. It is a well known result of ZFC (ZermeloFraenkel set theory with the axiom of choice AC) that ℵ1 is a regular cardinal, Form 34 in [1], (i.e., ℵ1 is not the limit of an i ..."
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Abstract. We study the relationship between various properties of the real numbers and weak choice principles. 1. Introduction. It is a well known result of ZFC (ZermeloFraenkel set theory with the axiom of choice AC) that ℵ1 is a regular cardinal, Form 34 in [1], (i.e., ℵ1 is not the limit of an increasing sequence (an)n∈ω of ordinals in ℵ1). On the other hand, this statement is not provable in ZFAC. Indeed, Form 34 implies that the real line R cannot be written as a countable union of countable subsets
Small examples of nonconstructible simplicial balls and spheres
 SIAM J. Discrete Math
, 2004
"... We construct nonconstructible simplicial dspheres with d + 10 vertices and nonconstructible, nonrealizable simplicial dballs with d + 9 vertices for d≥3. 1 ..."
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Cited by 14 (6 self)
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We construct nonconstructible simplicial dspheres with d + 10 vertices and nonconstructible, nonrealizable simplicial dballs with d + 9 vertices for d≥3. 1
Continuous truth I, nonconstructive objects
 In Proceedings of Logic Colloquium
, 1982
"... U.S.A. Aus t ra l ia We give a general theory of the log ic of po ten t i a l ly i n f i n i t e ob jec t s, derived from a theory of meaning f o r statements concerning these objec ts. main pa r t s which may be read independently but a r e intended t o complement each o the r. e s s e n t i a l l ..."
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Cited by 9 (1 self)
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U.S.A. Aus t ra l ia We give a general theory of the log ic of po ten t i a l ly i n f i n i t e ob jec t s, derived from a theory of meaning f o r statements concerning these objec ts. main pa r t s which may be read independently but a r e intended t o complement each o the r. e s s e n t i a l l y philosophical. In i t, we d iscuss the theory of meaning. We be l ieve t h a t even the s taunches t r e a l i s t must view poten t ia l i n f i n i t i e s opera t iona l ly. The second p a r t i s formal. In i t, we consider the in t e rp re t a t ion of log ic i n t he gros topos of sheaves over t he category of separable loca les equipped with the open cover topology. We show t h a t general p r inc ip l e s of cont inui ty, loca l choice and loca l compactness hold f o r these models. We conclude with a b r i e f discussion of the philosophical
Characterization of NonMonotone NonConstructive Systems
"... 1 Motivation Logical systems have traditionally been monotone. Artificial Intelligence has introduced nonmonotone systems. A crucial issue in connection with such systems is that of a characterizing theory. On the one hand, there have been proposals to weakening a theory of monotone systems so as ..."
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1 Motivation Logical systems have traditionally been monotone. Artificial Intelligence has introduced nonmonotone systems. A crucial issue in connection with such systems is that of a characterizing theory. On the one hand, there have been proposals to weakening a theory of monotone systems so as to make it encompass nonmonotone systems but the resulting theory trivially falls short of delineating nonmonotony. On the other hand, failure of monotony cannot serve as a founding feature because no theory worthy of the name is based on the mere absence of a property, which amounts to a negative definition. Scholars working in the field have been aware of this but seem to have overlooked the fact that some negative definitions can still be given a more valuable characterization. A famous example comes from lattice theory. Modular nondistributive lattices are of course those modular lattices that fail distributivity. This seems as negative as it can be. Yet, the very same class of lattice...
Results 1  10
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3,154