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UNITDISTANCE PRESERVING THEOREM IS LOGICALLY NONTRIVIAL
"... Abstract. If we express the statement of the unitdistance preserving theorem (that every mapping from R n to R n that preserves unit distance is linear) in terms of quantifiers and logical connectives, then we get a formula that is very close to formulas from elementary geometry. A. Tarski has prov ..."
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Abstract. If we express the statement of the unitdistance preserving theorem (that every mapping from R n to R n that preserves unit distance is linear) in terms of quantifiers and logical connectives, then we get a formula that is very close to formulas from elementary geometry. A. Tarski has
FIRST ORDER PRESERVATION THEOREMS IN TWOSORTED LANGUAGES
"... The purpose of this note is to extend to twosorted first order languages several wellknown onesorted preservation theorems, and to give some preservation theorems which are new even in the onesorted case. For reasons of uniformity and economy we adopt the presentation of Lindstrom [5]. However t ..."
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The purpose of this note is to extend to twosorted first order languages several wellknown onesorted preservation theorems, and to give some preservation theorems which are new even in the onesorted case. For reasons of uniformity and economy we adopt the presentation of Lindstrom [5]. However
Goldstern–Judah–Shelah preservation theorem for countable support iterations
, 1994
"... In [4] a preservation theorem for countable support iterated forcing is proved with restriction to forcing notions which are not ωdistributive. We give the proof of the theorem without this restriction. ..."
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Cited by 5 (0 self)
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In [4] a preservation theorem for countable support iterated forcing is proved with restriction to forcing notions which are not ωdistributive. We give the proof of the theorem without this restriction.
Preservation Theorems Concerning gHausdorff and rgHausdorff Spaces
, 2003
"... In this paper we introduce and study the concepts of topological spaces called gHausdorff and rgHausdorff spaces and investigate preservation theorems concerning gHausdorff and rgHausdorff spaces. ..."
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In this paper we introduce and study the concepts of topological spaces called gHausdorff and rgHausdorff spaces and investigate preservation theorems concerning gHausdorff and rgHausdorff spaces.
Permutations and Stratified formulae—a Preservation Theorem
, 2013
"... It is shown that the sentences (in the language of Set Theory) preserved by the construction usually used to prove the independence of the axiom of foundation can be characterised syntactically: they are precisely the formulae naturally expressible in the language of simple type theory. The permutat ..."
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It is shown that the sentences (in the language of Set Theory) preserved by the construction usually used to prove the independence of the axiom of foundation can be characterised syntactically: they are precisely the formulae naturally expressible in the language of simple type theory
Efficient similarity search in sequence databases
, 1994
"... We propose an indexing method for time sequences for processing similarity queries. We use the Discrete Fourier Transform (DFT) to map time sequences to the frequency domain, the crucial observation being that, for most sequences of practical interest, only the first few frequencies are strong. Anot ..."
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Cited by 515 (19 self)
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. Another important observation is Parseval's theorem, which specifies that the Fourier transform preserves the Euclidean distance in the time or frequency domain. Having thus mapped sequences to a lowerdimensionality space by using only the first few Fourier coe cients, we use Rtrees to index
Preservation theorems for GlivenkoCantelli and uniform GlivenkoCantelli classes
 134 In High Dimensional Probability II, Evarist Giné
, 2000
"... ABSTRACT We show that the P −Glivenko property of classes of functions F1,...,Fk is preserved by a continuous function ϕ from R k to R in the sense that the new class of functions x → ϕ(f1(x),...,fk(x)), fi ∈Fi, i =1,...,k is again a GlivenkoCantelli class of functions if it has an integrable envel ..."
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Cited by 27 (11 self)
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envelope. We also prove an analogous result for preservation of the uniform GlivenkoCantelli property. Corollaries of the main theorem include two preservation theorems of Dudley (1998). We apply the main result to reprove a theorem of Schick and Dudley 1998a or b? Yu (1999)concerning consistency
AN ALGEBRAIC PRESERVATION THEOREM FOR ℵ0CATEGORICAL QUANTIFIED CONSTRAINT SATISFACTION
, 2012
"... Vol. 9(1:15)2013, pp. 1–23 www.lmcsonline.org ..."
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