AbstractIn this paper the existence of a real closure of an ordered field is given without the use of the axiom of choice. The possibility of such a proof and related results demonstrate fundamental differences between the concepts of real and algebraic closures of fields
We give a general method for producing various effective Null and Positivstellensätze, and getting n...
When reasoning formally with polynomials over real numbers, or more generally real closed fields, we...
AbstractThe paper shows elimination of imaginaries for real closed valued fields to suitable sorts. ...
In this paper, we shall study certain natural generalizations of the concept of real closure, replac...
Abstract"Closures" and "orders" of fields which are not necessarily formally real are introduced her...
International audienceThis paper describes a generalization of the real closure computation of an or...
Let ℒ be the first order language of field theory with an additional one place predicate symbol. In ...
AbstractThe existing algorithms to construct the real closure of an ordered field involve very high ...
AbstractLet K be a field, and let W(K) denote its Witt ring of Quadratic Forms. It is well-known in ...
The following conjecture is due to Shelah-Hasson: Any infinite strongly NIP field is either real clo...
We extend the algebraic theory of ordered fields [7, 6] in Mizar [1, 2, 3]: we show that every preor...
We recall that an ordered field is a field which has a linear order and the order topology (by this ...
In this chapter we introduce a primary tool for dealing with in\u85nite preordered sets. This is the...
Shepherdson [14] showed that for a discrete ordered ring I , I is a model of IOpen iff I is an integ...
The purpose of this thesis is to study the concept of completeness in an ordered field. Several con...
We give a general method for producing various effective Null and Positivstellensätze, and getting n...
When reasoning formally with polynomials over real numbers, or more generally real closed fields, we...
AbstractThe paper shows elimination of imaginaries for real closed valued fields to suitable sorts. ...
In this paper, we shall study certain natural generalizations of the concept of real closure, replac...
Abstract"Closures" and "orders" of fields which are not necessarily formally real are introduced her...
International audienceThis paper describes a generalization of the real closure computation of an or...
Let ℒ be the first order language of field theory with an additional one place predicate symbol. In ...
AbstractThe existing algorithms to construct the real closure of an ordered field involve very high ...
AbstractLet K be a field, and let W(K) denote its Witt ring of Quadratic Forms. It is well-known in ...
The following conjecture is due to Shelah-Hasson: Any infinite strongly NIP field is either real clo...
We extend the algebraic theory of ordered fields [7, 6] in Mizar [1, 2, 3]: we show that every preor...
We recall that an ordered field is a field which has a linear order and the order topology (by this ...
In this chapter we introduce a primary tool for dealing with in\u85nite preordered sets. This is the...
Shepherdson [14] showed that for a discrete ordered ring I , I is a model of IOpen iff I is an integ...
The purpose of this thesis is to study the concept of completeness in an ordered field. Several con...
We give a general method for producing various effective Null and Positivstellensätze, and getting n...
When reasoning formally with polynomials over real numbers, or more generally real closed fields, we...
AbstractThe paper shows elimination of imaginaries for real closed valued fields to suitable sorts. ...
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