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23,469
Openclosed field algebras
, 2007
"... We introduce the notions of openclosed field algebra and openclosed field algebra over a vertex operator algebra V. In the case that V satisfies certain finiteness and reductivity conditions, we show that an openclosed field algebra over V canonically gives an algebra over a Cextension of Swiss ..."
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Cited by 30 (10 self)
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We introduce the notions of openclosed field algebra and openclosed field algebra over a vertex operator algebra V. In the case that V satisfies certain finiteness and reductivity conditions, we show that an openclosed field algebra over V canonically gives an algebra over a Cextension of Swiss
Intersections of real closed fields
 Canadian J. Math
, 1980
"... 1. In this paper we wish to study fields which can be written as intersections of real closed fields. Several more restrictive classes of fields have received careful study (real closed fields by Artin and Schreier, hereditarily euclidean fields by Prestel and Ziegler [8], hereditarily Pythagorea ..."
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Cited by 4 (4 self)
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1. In this paper we wish to study fields which can be written as intersections of real closed fields. Several more restrictive classes of fields have received careful study (real closed fields by Artin and Schreier, hereditarily euclidean fields by Prestel and Ziegler [8], hereditarily Pythago
Algebraically Closed Fields
"... 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
 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. ..."
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Cited by 7 (0 self)
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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
, 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 ..."
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Cited by 4 (3 self)
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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
"... 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 Lrational po ..."
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Cited by 3 (2 self)
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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
 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 rKreducibility, forms a countable real closed subfield of the real ordered field. This generalizes the wellknown fact that the computable reals form a real closed field. With the same techniq ..."
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Cited by 4 (1 self)
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Abstract. We show that for any real number, the class of real numbers less random than it, in the sense of rKreducibility, forms a countable real closed subfield of the real ordered field. This generalizes the wellknown fact that the computable reals form a real closed field. With the same
The irreducibility of the space of curves of given genus
 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 ~ ..."
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Cited by 506 (2 self)
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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
, 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 ..."
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Cited by 1 (0 self)
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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
Results 1  10
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23,469