Daniel Lewis, Maria João Zilhão, Nia Jones, Daniel Lewis, Carlos Marcelo, Albano Miranda, ...
EUROPEAN COMMISSION EUROSTAT Handbook on improving quality by analysis of process variables Alexis Aitken, Jan Hörngren, Nia Jones,
Weakly o-minimal structures and real closed fields (2008)
Dugald Macpherson, David Marker, Charles Steinhorn
Abstract. A linearly ordered structure is weakly o-minimal if all of its definable sets in one variable are the union of finitely many convex sets in the structure. Weakly o-minimal structures were...
The Borel Complexity of Ismomorphism for Theories with Many Types ∗ (2008)
Kechris asked which Borel equivalence relations can arise as the isomorphism relation for models of a first order theory. In particular, they asked if the isomorphism relation can be essentially...
Model Theory and Real Exponentiation (2007)
This paper is based on an invited lecture presented in October 1994 at the AMS Central regional meeting in Stillwater Oklahoma.
A Failure of Quantifier Elimination (2007)
Angus Macintyre, David Marker, Let L
uld actually eliminate quantifiers in the language L an [ flogg [ fx q : q 2 Qg. Here we show that although exp and log are interdefinable, log is essential for quantifer elimination. Theorem. Let...
Logarithmic-exponential series (2007)
Abstract. We extend the field of Laurent series over the reals in a canonical way to an ordered differential field of "LE-series " (logarithmic-exponential series), which is...
David Marker Fall, David Marker
en Xn is a Polish space. Suppose dn is a complete metric on Xn , with dn < 1, for n = 0; 1; : : :. De ne b d on Xn by b d(f; g) = n+1 dn (f(n); g(n)): If f 0 ; f 1 ; : : : is a Cauchy-sequence,...
The Borel Complexity of Isomorphism for Theories with Many Types (2007)
During the Notre Dame workshop on Vaught's Conjecture, Hjorth and Kechris asked which Borel equivalence relations can arise as the isomorphism relation for countable models of a first-order theory....
The Number of Countable Differentially Closed Fields (2007)
We outline the Hrushovsk-Sokolović proof of Vaught's Conjecture for differentially closed fields, focusing on the use of dimensions to code graphs.
Decidability of the Natural Numbers with the Almost-All Quantifier (2006)
Marker, David, Slaman, Theodore A.
We consider the fragment F of first order arithmetic in which quantification is restricted to ''for all but finitely many.'' We show that the integers form an F-elementary substructure of the real...
Decidability of the Natural Numbers with the Almost-All Quantifier (2006)
David Marker, Theodore A. Slaman
We consider the fragment F of first order arithmetic in which quantification is restricted to “for all but finitely many. ” We show that the integers form an F-elementary substructure of the real...
Decidability of the Natural Numbers with the Almost-All Quantifier (2006)
David Marker, Theodore A. Slaman
We consider the fragment F of first order arithmetic in which quantification is restricted to “for all but finitely many. ” We show that the integers form an F-elementary substructure of the real...
A conversation with Joseph Waksberg (2000)
Marker, David, Morganstein, David
Joseph Waksberg was born September 20, 1915, in Kielce, Poland; his family emigrated to the United States in 1921. Soon after graduating from the City University of New York CUNY in 1936, he moved to...
n and Phyllis Cassidy for helpful discussions on this subject. None of the results presented here are new. My main goal is to give a coherent exposition of these matters. Let K be a dierentially...
Strongly Minimal Sets and Geometry (1998)
F12.24> OE(a) /(a)g and fa 2 N : N j= OE(a) :/(a)g is infinite. We say that a subset D of M n is strongly minimal if it is defined by a strongly minimal formula. We will often consider D as a...
David Marker, Margit Messmer, Anand Pillay, Anand Pillay
varieties are the algebraic-geometric analog of manifolds. Clearly affine and projective varieties are examples of abstract varieties, as are open subsets of projective varieties. We drop the...
Differential Galois Theory III: some inverse problems. (1996)
In [16] a theory of generalised strongly... In this paper we initiate a study of the inverse problem for generalised strongly normal extensions. We will henceforth call generalised strongly normal...
Model Theory Of Differential Fields (1996)
2.03> D(a) = D(b \Delta a b ) = bD( a b ) + a b D(b). Thus D( a b ) = 1 b D(a) \Gamma a b 2 D(b) = bD(a)\GammaaD(b) b 2 . examples. 1) (trivial derivation) D : R ! f0g. 2) Let C 1 be the ring of...
Model theory and exponentiation (1996)
Model theory is a branch of mathematical logic in which one studies mathematical structures by considering the first-order sentences true of those structures and the sets definable in those...
Logarithmic-Exponential Power Series
. We use generalized power series to construct algebraically a nonstandard model of the theory of the real field with exponentiation. This model enables us to show the undefinability of the zeta...
Logarithmic-Exponential Series
. We extend the eld of Laurent series over the reals in a canonical way to an ordered dierential eld of \LE-series" (logarithmic-exponential series), which is equipped with a well behaved...