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closed fields

by Cyril Cohen, Assia Mahboubi, Inria Saclay Île-de-france, Lix École Polytechnique , 2010
"... A formal quantifier elimination for algebraically ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
A formal quantifier elimination for algebraically

Open-closed field algebras

by Liang Kong , 2007
"... We introduce the notions of open-closed field algebra and open-closed field algebra over a vertex operator algebra V. In the case that V satisfies certain finiteness and reductivity conditions, we show that an open-closed field algebra over V canonically gives an algebra over a C-extension of Swiss- ..."
Abstract - Cited by 30 (10 self) - Add to MetaCart
We introduce the notions of open-closed field algebra and open-closed field algebra over a vertex operator algebra V. In the case that V satisfies certain finiteness and reductivity conditions, we show that an open-closed field algebra over V canonically gives an algebra over a C-extension of Swiss

Intersections of real closed fields

by Thomas C. Craven - Canadian J. Math , 1980
"... 1. In this paper we wish to study fields which can be written as inter-sections of real closed fields. Several more restrictive classes of fields have received careful study (real closed fields by Artin and Schreier, hered-itarily euclidean fields by Prestel and Ziegler [8], hereditarily Pythago-rea ..."
Abstract - Cited by 4 (4 self) - Add to MetaCart
1. In this paper we wish to study fields which can be written as inter-sections of real closed fields. Several more restrictive classes of fields have received careful study (real closed fields by Artin and Schreier, hered-itarily euclidean fields by Prestel and Ziegler [8], hereditarily Pythago

Algebraically Closed Fields

by Thierry Coquand
"... Algebraic closure In the previous lecture, we have seen how to “force ” the existence of prime ideals, even in a weark framework where we don’t have choice axiom Instead of “forcing ” the existence of a point of a space (a mathematical object), we are going to “force ” the existence of a model (a ma ..."
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Algebraic closure In the previous lecture, we have seen how to “force ” the existence of prime ideals, even in a weark framework where we don’t have choice axiom Instead of “forcing ” the existence of a point of a space (a mathematical object), we are going to “force ” the existence of a model (a mathematical structure)

Projective planes in algebraically closed fields

by David M. Evans, Ehud Hrushovski - Proc. London Math. Soc , 1991
"... We investigate the combinatorial geometry obtained from algebraic closure over a fixed subfield in an algebraically closed field. The main result classifies the subgeometries which are isomorphic to projective planes. This is applied to give new examples of algebraic characteristic sets of matroids. ..."
Abstract - Cited by 7 (0 self) - Add to MetaCart
We investigate the combinatorial geometry obtained from algebraic closure over a fixed subfield in an algebraically closed field. The main result classifies the subgeometries which are isomorphic to projective planes. This is applied to give new examples of algebraic characteristic sets of matroids

Generalizing Theorems in Real Closed Fields

by Matthias Baaz, Richard Zach , 1995
"... Jan Krajicek posed the following problem: Is there is a generalization result in the theory of real closed fields of the form: If A(1 + ... + 1) (n occurrences of 1) is provable in length k for all n, then (x)A(x) is provable? It is argued that the answer to this question depends on the particular f ..."
Abstract - Cited by 4 (3 self) - Add to MetaCart
Jan Krajicek posed the following problem: Is there is a generalization result in the theory of real closed fields of the form: If A(1 + ... + 1) (n occurrences of 1) is provable in length k for all n, then (x)A(x) is provable? It is argued that the answer to this question depends on the particular

GROUPS DEFINABLE IN SEPARABLY CLOSED FIELDS

by E. Bouscaren, F. Delon
"... Abstract. We consider the groups which are infinitely definable in separably closed fields of finite degree of imperfection. We prove in particular that no new definable groups arise in this way: we show that any group definable in such a field L is definably isomorphic to the group of L-rational po ..."
Abstract - Cited by 3 (2 self) - Add to MetaCart
Abstract. We consider the groups which are infinitely definable in separably closed fields of finite degree of imperfection. We prove in particular that no new definable groups arise in this way: we show that any group definable in such a field L is definably isomorphic to the group of L

Relative randomness and real closed fields

by Alexander Raichev - J. Symbolic Logic , 2005
"... Abstract. We show that for any real number, the class of real numbers less random than it, in the sense of rK-reducibility, forms a countable real closed subfield of the real ordered field. This generalizes the well-known fact that the computable reals form a real closed field. With the same techniq ..."
Abstract - Cited by 4 (1 self) - Add to MetaCart
Abstract. We show that for any real number, the class of real numbers less random than it, in the sense of rK-reducibility, forms a countable real closed subfield of the real ordered field. This generalizes the well-known fact that the computable reals form a real closed field. With the same

The irreducibility of the space of curves of given genus

by P. Deligne, D. Mumford - Publ. Math. IHES , 1969
"... Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~- ..."
Abstract - Cited by 506 (2 self) - Add to MetaCart
Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k

Imaginaries in pairs of algebraically closed fields

by Anand Pillay , 2006
"... We consider the theory (ACFp)P of pairs F < K of algebraically closed fields of a given characteristic p. We exhibit a collection of additional sorts in which this theory has geometric elimination of imaginaries. The sorts are essentially of the form ∪ a∈B(F)Va(K)/Ga(F), where G, V, B are varieti ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
We consider the theory (ACFp)P of pairs F < K of algebraically closed fields of a given characteristic p. We exhibit a collection of additional sorts in which this theory has geometric elimination of imaginaries. The sorts are essentially of the form ∪ a∈B(F)Va(K)/Ga(F), where G, V, B
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