Infinite finitely generated fields are bi-interpretable with N (2009)
Abstract. Using the work of several other mathematicians, principally the results of Poonen refining the work of Pop that algebraic independence is definable within the class of finitely generated...
Strongly minimal groups in the theory of compact complex spaces (2009)
Matthias Aschenbrenner, Rahim Moosa, Thomas Scanlon
Abstract. We characterise strongly minimal groups interpretable in elementary extensions of compact complex analytic spaces. 1.
Generalised Hasse varieties and their jet spaces (2009)
This work provides a unified formalism for studying difference and (Hasse-) differential algebraic geometry, by introducing a theory of "iterative Hasse rings and schemes". As an application, Hasse...
Medvedev, Alice, Scanlon, Thomas
We study algebraic dynamical systems (and, more generally, $\sigma$-varieties) $\Phi:{\mathbb A}^n_{\mathbb C} \to {\mathbb A}^n_{\mathbb C}$ given by coordinatewise univariate polynomials,...
Analytic relations on a dynamical orbit (2008)
Let $(K,|\cdot|)$ be a complete discretely valued field and $f:{\mathbb B}_1(K,1) \to {\mathbb B}_1(K,1)$ a nonconstant analytic map from the unit back to itself. We assume that 0 is an attracting...
Compact complex manifolds with the DOP and other properties (2008)
We point out that a certain complex compact manifold constructed by Lieberman has the dimensional order property, and has U-rank different from Morley rank. We also give a sufficient condition for a...
SUPERSTABILITY OF F-STRUCTURES (2008)
The following note is a supplement to [1]. We will maintain the notation of [1] throughout, and all numbered items to which we refer are from that paper. Theorem 6.11 states that if M is a finitely...
MODEL THEORY AND DIFFERENTIAL ALGEBRA (2008)
I survey some of the model-theoretic work on differential algebra and related topics. 1
INFINITE STABLE FIELDS ARE ARTIN-SCHREIER CLOSED (2008)
Abstract. We note that if K is an infinite stable field of characteristic p> 0, then the Artin-Schreier map ℘ : K → K given by x ↦ → x p − x is surjective. Consequently, K has no finite...
Nonstandard meromorphic groups (2008)
Extending the work of [7] on groups definable in compact complex manifolds and of [1] on strongly minimal groups definable in nonstandard compact complex manifolds, we classify all groups definable...
DIFFERENTIALLY VALUED FIELDS ARE NOT DIFFERENTIALLY CLOSED (2008)
Abstract. In answer to a question of L. van den Dries, we show that no differentially closed field possesses a differential valuation. 1.
Abstract. We show that a connected group interpretable in a compact complex manifold (a meromorphic group) is definably an extension of a complex torus by a linear algebraic group, generalizing...
manuscripta mathematica manuscript No. (will (2008)
Thomas Scanlon, José Felipe Voloch
be inserted by the editor)
Local André-Oort conjecture for the universal abelian variety (2008)
Abstract. We prove a p-adic analogue of the André-Oort conjecture for subvarieties of the universal abelian varieties containing a dense set of special points. Let g and n be integers with n ≥ 3...
Strongly minimal groups in the theory of compact complex spaces (2008)
Matthias Aschenbrenner, Rahim Moosa, Thomas Scanlon
Abstract. We characterise strongly minimal groups interpretable in elementary extensions of compact complex analytic spaces. 1.
ALGEBRAIC RELATIONS AMONGST PERIODIC POINTS OF A LIFTING OF FROBENIUS (2008)
Abstract. Let p be a prime number and f ∈ Zp[x] a polynomial over the p-adic integers lifting the Frobenius in the sense that f(x) ≡ xp (mod p) and deg(f) = p. Let Πf: = {ζ ∈ Q alg p: f ◦n...
FIELDS ADMITTING NONTRIVIAL STRONG ORDERED EULER CHARACTERISTICS ARE QUASIFINITE (2008)
The note contains the details of an assertion made in [1] to the effect that fields admitting a nontrivial strong ordered Euler characteristic are quasifinite. In this section we recall the relevant...
Infinite finitely generated fields are bi-interpretable with N (2008)
Abstract. Using the work of several other mathematicians, principally the results of Poonen refining the work of Pop that algebraic independence is definable within the class of finitely generated...
We show that a connected group interpretable in a compact complex manifold (a meromorphic group) is definably an extension of a complex torus by a linear algebraic group, generalizing results in [4]....
Abstract. Let X be an algebraic variety over the algebraically closed field K and Ξ ⊆ X(K) a set of K-rational points on X. We say that a subvariety Y ⊆ X n of some Cartesian power of X is...
POSITIVE CHARACTERISTIC MANIN-MUMFORD THEOREM (2008)
Abstract. We present the details of a model theoretic proof of an analogue of the Manin-Mumford conjecture for semiabelian varieties in positive characteristic. As a by-product of the proof we reduce...
Public key cryptosystems based on Drinfeld modules are insecure (2008)
Abstract. We show that analogues of popular public key cryptosystems based on Drinfeld modules are insecure by providing polynomial time algorithms to solve the Drinfeld module versions of the...
POSITIVE CHARACTERISTIC MANIN-MUMFORD THEOREM (2008)
Abstract. We present the details of a model theoretic proof of an analogue of the Manin-Mumford conjecture for semiabelian varieties in positive characteristic. As a by-product of the proof we reduce...
Abstract. Let X be an algebraic variety over the algebraically closed field K and Ξ ⊆ X(K) a set of K-rational points on X. We say that a subvariety Y ⊆ X n of some Cartesian power of X is...
Combinatorics With Definable Sets: Euler Characteristics And Grothendieck Rings (2007)
Jan Krajícek, I Cek, Thomas Scanlon
. We recall the notions of weak and strong Euler characteristics on a rst order structure and make explicit the notion of a Grothendieck ring of a structure. We dene partially ordered Euler...
Compact complex manifolds with the DOP and other properties (2007)
We point out that a certain complex compact manifold constructed by Lieberman has the dimensional order property, and has U-rank different from Morley rank. We also give a sufficient condition for a...
Public key cryptosystems based on Drinfeld modules are insecure (2007)
Abstract. We show that analogues of popular public key cryptosystemsbased on Drinfeld modules are insecure by providing polynomial time algorithms to solve the Drinfeld module versions of the...
Abstract. Tate and Voloch have conjectured that the p-adic distance from torsion points of semi-abelian varieties over C p to subvarieties may be uniformly bounded. We prove this conjecture for...
Abstract. Buium proved what he called the abc theorem for abelian varieties over function elds in characteristic zero [3]. Using methods of algebraic model theory we prove an analog of his theorem...
Quanti er Elimination for the Relative Frobenius (2007)
Abstract. Let (K;v) be a complete discretely valued eld of characteristic zero with an algebraically closed residue eld of positive characteristic. Let : K! K be a continuous automorphism of K...
We show that a connected group interpretable in a compact complex manifold (a meromorphic group) is denably an extension of a complex torus by a linear algebraic group, generalizing results in [4]. A...
FIELDS ADMITTING NONTRIVIAL STRONG ORDERED EULER CHARACTERISTICS ARE QUASIFINITE (2007)
The note contains the details of an assertion made in [1] to the eect that elds admitting a nontrivial strong ordered Euler characteristic are quasinite. In this section we recall the relevant...
Abstract. We note that if K is an innite stable eld of characteristic p> 0, then the Artin-Schreier map} : K! K given by x 7! x p x is surjective. Consequently, K has no nite Galois extensions of...
COMBINATORICS WITH DEFINABLE SETS: EULER CHARACTERISTICS AND GROTHENDIECK RINGS (2007)
Jan Kraj, I Cek, Thomas Scanlon
Abstract. We recall the notions of weak and strong Euler characteristics on a rst order structure and make explicit the notion of a Grothendieck ring of a structure. We dene partially ordered Euler...
Superstability Of F-Structures (2007)
Rahim Moosa And, Rahim Moosa, Thomas Scanlon, Exp M
sets: Definition 0.2. If S Exp M then the dimension of S, denoted by dim S, is the #-dimension of S for any # > 0 a multiple of # M such that S Exp M (#). Lemma 0.3. Suppose S 1 , . . . , Sn , T 1...
Positive Characteristic Manin-Mumford Theorem (2007)
We present the details of a model theoretic proof of an analogue of the Manin-Mumford conjecture for semiabelian varieties in positive characteristic.
Model theory of the Frobenius on the Witt vectors (2007)
Bélair, Luc., Scanlon, Thomas.
American Journal of Mathematics - Volume 129, Number 3, June 2007
Differential arcs and regular types in differential fields (2007)
Rahim Moosa, Anand Pillay, Thomas Scanlon
Abstract. We introduce differential arc spaces in analogy to the algebraic arc spaces and show that a differential variety is determined by its arcs at a point. Using differential arcs, we show that...
Luc Bélair, Angus Macintyre, Thomas Scanlon
Abstract. We give axiomatizations and prove quantifier elimination theorems for first-order theories of unramified valued fields with an automorphism having a close interaction with the valuation. We...
Differential arcs and regular types in differential fields (2007)
Rahim Moosa, Anand Pillay, Thomas Scanlon
Abstract. We introduce differential arc spaces in analogy to the algebraic arc spaces and show that a differential variety is determined by its arcs at a point. Using differential arcs, we show that...
Strongly minimal groups in the theory of compact complex spaces (2006)
Aschenbrenner, Matthias, Moosa, Rahim, Scanlon, Thomas
We characterise strongly minimal groups interpretable in elementary extensions of compact complex analytic spaces.
Barriers for HIV testing during pregnancy in Southern Brazil (2006)
Rosa,Humberto, Goldani,Marcelo Zubaran, Scanlon,Thomas, Giugliani,Elsa Justo, Agranonik,Marilyn, ...
OBJECTIVE: To assess HIV testing rate and determine risk factors for not have been tested during pregnancy. METHODS: A cross-sectional study was carried out in Porto Alegre, Southern Brazil, from...
Contractualismo y utilitarismo (2006)
En este artículo de 1982, Thomas Scanlon esboza una explicación filosófica de los deberes morales recíprocos que alcanza su exposición completa, con algunos cambios, en 1998 con el libro What We...
Local Andr\'{e}-Oort conjecture for the universal abelian variety (2004)
We prove a $p$-adic analogue of the Andr\'{e}-Oort conjecture for subvarieties of the universal abelian varieties containing a dense set of special points. Let $g$ and $n$ be integers with $n \geq 3$...
F -structures and integral points on semiabelian varieties over finite fields (2004)
Moosa, Rahim., Scanlon, Thomas.
American Journal of Mathematics - Volume 126, Number 3, June 2004
Let X be an algebraic variety over the algebraically closed field K and Ξ ⊆ X(K) a set of K-rational points on X. We say that a subvariety Y ⊆ Xn of some Cartesian power of X is Ξ-special if...
Voluntary HIV counseling and testing during prenatal care in Brazil (2003)
Goldani,Marcelo Zubaran, Giugliani,Elsa Regina Justo, Scanlon,Thomas, Rosa,Humberto, Castilhos,Kelli, Feldens,Letícia, ...
OBJECTIVE: Voluntary HIV counseling and testing are provided to all Brazilian pregnant women with the purpose of reducing mother-to-child HIV transmission. The purpose of the study was to assess...
Positive characteristic Manin-Mumford theorem (2003)
We prove a version of the Manin-Mumford conjecture for semiabelian varieties over fields of positive characteristic. The proof presented here contains the details of the proof sketched by the author...
The Mordell-Lang conjecture in positive characteristic revisited (2003)
Abstract. We describe intersections of finitely generated subgroups of semi-abelian varieties with subvarieties in characteristic p. 1.
SUPERSTABILITY OF F-STRUCTURES (2003)
The following note is a supplement to [1]. We will maintain the notation of [1] throughout, and all numbered items to which we refer are from that paper. Theorem 6.11 states that if M is a finitely...
F -structures and integral points on semiabelian varieties over finite fields (2003)
Abstract. Motivated by the problem of determining the structure of integral points on subvarieties of semiabelian varieties defined over finite fields, we prove a quantifier elimination and stability...
F -structures and integral points on semiabelian varieties over finite fields (2003)
Abstract. Motivated by the problem of determining the structure of integral points on subvarieties of semiabelian varieties defined over finite fields, we prove a quantifier elimination and stability...
The Mordell-Lang conjecture in positive characteristic revisited (2003)
Abstract. We prove versions of the Mordell-Lang conjecture for semiabelian varieties defined over fields of positive characteristic.
The Mordell-Lang Conjecture in Positive Characteristic Revisited (2003)
We prove versions of the Mordell-Lang conjecture for semiabelian varieties de ned over elds of positive characteristic.
F-Structures And Integral Points On Semiabelian (2003)
Varieties Over Finite, Rahim Moosa, Thomas Scanlon
Motivated by the problem of determining the structure of integral points on subvarieties of semiabelian varieties defined over finite fields, we prove a quantifier elimination and stability result...
F -structures and integral points on semiabelian varieties over finite fields (2003)
Abstract. Motivated by the problem of determining the structure of integral points on subvarieties of semiabelian varieties defined over finite fields, we prove a quantifier elimination and stability...
F-structures and integral points on semiabelian varieties over finite fields (2002)
Motivated by the problem of determining the structure of integral points on subvarieties of semiabelian varieties defined over finite fields, we prove a quantifier elimination result for certain...
Model theory of the Frobenius on the Witt vectors (2002)
Luc Bélair, Angus Macintyre, Thomas Scanlon
We give axiomatizations and quantifier eliminations for first-order theories of finitely ramified valued fields with an automorphism having a close interaction with the valuation. We achieve an...
Uniformity in the Mordell-Lang conjecture (2001)
We note that Pillay's result on the stability of an algebraically closed field with a predicate for a group of Lang type implies that number uniformity follows formally from the finiteness results...
Diophantine geometry from model theory (2001)
$1. Introduction. With Hrushovski's proof of the function field MordellLang conjecture [16] the relevance of geometric stability theory to diophantine geometry first came to light. A gulf...
Diophantine geometry from model theory (2001)
With Hrushovski's proof of the function eld Mordell-Lang conjecture [13] the relevance of geometric stability theory to diophantine geometry rst came to light. A gulf between logicians and...
Diophantine geometry from model theory (2001)
With Hrushovski’s proof of the function field Mordell-Lang conjecture [13] the relevance of geometric stability theory to diophantine geometry first came to light. A gulf between logicians and...
Model Theory and Differential Algebra (2001)
This paper stems from my lecture notes for a talk given at Rutgers University in Newark on 3 November 2000 as part of the Workshop on Dierential Algebra and Related Topics. I thank Li Guo for...
Pillay, Anand, Scanlon, Thomas
We introduce the notion of a meromorphic group, weakening somewhat Fujiki's definition We prove that a meromorphic group is meromorphically an extension of a complex torus by a linear algebraic...
We introduce the notion of a meromorphic group, weakening somewhat Fujiki's definition ([4]). We prove that a meromorphic group is meromorphically an extension of a complex torus by a linear...
Combinatorics with definable sets: Euler characteristics and Grothendieck rings (2000)
Abstract. We recall the notions of weak and strong Euler characteristics on a first order structure and make explicit the notion of a Grothendieck ring of a structure. We define partially ordered...
• (hyper-)graph theoretic/combinatorial version • additive invariant of definable sets 3 O-minimal structures Definition 1 A linearly ordered structure M = (M, <, · · · ) in language...
The conjecture of Tate and Voloch on p-adic proximity to torsion (1999)
Abstract. Tate and Voloch have conjectured that the p-adic distance from torsion points of semi-abelian varieties over C p to subvarieties may be uniformly bounded. We prove this conjecture for...
Quantifier elimination for the relative Frobenius (1999)
Abstract. Let (K; v) be a complete discretely valued field of characteristic zero with an algebraically closed residue field of positive characteristic. Let oe: K! K be a continuous automorphism of K...
Quantifier elimination for the relative Frobenius (1999)
Abstract. Let (K;v) be a complete discretely valued field of characteristic zero with an algebraically closed residue field of positive characteristic. Let oe: K! K be a continuous automorphism of K...
Diophantine geometry of the torsion of a Drinfeld module, preprint (1999)
Abstract. We prove an analogue of the Manin-Mumford conjecture for Drinfeld modules of generic characteristic. 1.
Quantifier elimination for the relative Frobenius (1999)
Abstract. Let (K, v) be a complete discretely valued field of characteristic zero with an algebraically closed residue field of positive characteristic. Let σ: K → K be a continuous automorphism...
The conjecture of Tate and Voloch on p-adic proximity to torsion (1999)
Abstract. Tate and Voloch have conjectured that the p-adic distance from torsion points of semi-abelian varieties over Cp to subvarieties may be uniformly bounded. We prove this conjecture for...
Lascar and Morley ranks differ in differentially closed fields (1999)
Ehud Hrushovski, Thomas Scanlon
We note here, in answer to a question of Poizat, that the Morley and Lascar ranks need not coin-cide in differentially closed fields. We will approach this through the (perhaps) more fundamental...
Diophantine geometry of the torsion of a Drinfeld module, preprint (1999)
Abstract. We prove an analogue of the Manin-Mumford conjecture for Drinfeld modules of generic characteristic. 1.
Quantifier elimination for the relative Frobenius (1999)
Abstract. Let (K, v) be a complete discretely valued field of characteristic zero with an algebraically closed residue field of positive characteristic. Let σ: K → K be a continuous automorphism...
Difference subgroups of commutative algebraic groups over finite fields (1998)
Scanlon, Thomas, Voloch, José Felipe
The work of Chatzidakis and Hrushovski on the model theory of difference fields in characteristic zero showed that groups defined by difference equations have a very restricted structure. Recent work...
Supersimple fields and division rings (1998)
Pillay, Anand, Scanlon, Thomas, Wagner, Frank
It is proved that any supersimple field has trivial Brauer group, and more generally that any supersimple division ring is commutative. As prerequisites we prove several results about generic types...
Lascar and Morley ranks differ in differentially closed fields (1998)
Hrushovski, Ehud, Scanlon, Thomas
We note here, in answer to a question of Poizat, that the Morley and Lascar ranks need not coincide in differentially closed fields. We approach this through the (perhaps) more fundamental issue of...
Abstract. Tate and Voloch have conjectured that the p-adic distance from torsion points of semi-abelian varieties over Cp to subvarieties may be uniformly bounded. We prove this conjecture for...
Model theory of valued D-fields (1997)
Abstract. The notion of a D-ring, generalizing that of a dierential or a dierence ring, is introduced. Quantier elimination and a version of the AxKochen-Ershov principle is proven for a theory of...
Model theory of valued D-fields (1997)
Abstract. The notion of a D-ring, generalizing that of a differential or a difference ring, is introduced. Quantifier elimination and a version of the AxKochen-Ershov principle is proven for a theory...
Model theory of valued D-fields (1997)
Abstract. The notion of a D-ring, generalizing that of a differential or a difference ring, is introduced. Quantifier elimination and a version of the Ax-Kochen-Ershov principle is proven for a...
The abc theorem for commutative algebraic groups in characteristic p (1997)
Abstract. Buium proved what he called the abc theorem for abelian varieties over function fields in characteristic zero [3]. Using methods of algebraic model theory we prove an analog of his theorem...
Cohen, Marshall, Nagel, Thomas, Scanlon, Thomas
Incluye bibliografía
A unified treatment of elementary proof theory /--by Thomas Michael Scanlon, Jr. (1968)
Photocopy. Cambridge, Mass. : Harvard University Archives [1975?]
A unified treatment of elementary proof theory.
Thesis (Ph. D.)--Harvard University, 1968.