Add to ORKGThe purpose of this thesis is to study the concept of completeness in an ordered field. Several conditions which are necessary and sufficient for completeness in an ordered field are examined. In Chapter I the definitions of a field and an ordered field are presented and several properties of fields and ordered fields are noted. Chapter II defines an Archimedean field and presents several conditions equivalent to the Archimedean property. Definitions of a complete ordered field (in terms of a least upper bound) and the set of real numbers are also stated. Chapter III presents eight conditions which are equivalent to completeness in an ordered field. These conditions include the concepts of nested intervals, Dedekind cuts, bounded monotonic...
Nested intervals and completeness are investigated in infinitesimal extensions of ordered sets
The Dedekind cuts in an ordered set form a set in the sense of constructive Zermelo-Fraenkel set the...
This work aims to show the existence and Uniqueness of the field of Real Numbers, using for this, D...
summary:An ordered field is a field which has a linear order and the order topology by this order. F...
In this paper, we present some basic facts concerning ordered fields. We review definitions of an or...
We recall that an ordered field is a field which has a linear order and the order topology (by this ...
By using the preliminary results given in a previous divulgative note, we present here a concise and...
Abstract. Given a Dedekind incomplete ordered field, a pair of convergent nets of gaps which are res...
The effective content of ordered fields is investigated using tools of computability theory and reve...
The purpose of this paper was to prove the equivalence of the following completeness axioms. This pu...
In this paper, we shall study certain natural generalizations of the concept of real closure, replac...
Let 2F and Jf be ordered fields such that & is a sub-field of Jf. JT is said to be Archimedean o...
Abstract. We explore the distinction between convergence and absolute con-vergence of series in both...
In this paper the main results are :Proofs that the ordinal real numbers are real closed fields and ...
In this paper the main results are :Proofs that the ordinal real numbers are real closed fields and ...
Nested intervals and completeness are investigated in infinitesimal extensions of ordered sets
The Dedekind cuts in an ordered set form a set in the sense of constructive Zermelo-Fraenkel set the...
This work aims to show the existence and Uniqueness of the field of Real Numbers, using for this, D...
summary:An ordered field is a field which has a linear order and the order topology by this order. F...
In this paper, we present some basic facts concerning ordered fields. We review definitions of an or...
We recall that an ordered field is a field which has a linear order and the order topology (by this ...
By using the preliminary results given in a previous divulgative note, we present here a concise and...
Abstract. Given a Dedekind incomplete ordered field, a pair of convergent nets of gaps which are res...
The effective content of ordered fields is investigated using tools of computability theory and reve...
The purpose of this paper was to prove the equivalence of the following completeness axioms. This pu...
In this paper, we shall study certain natural generalizations of the concept of real closure, replac...
Let 2F and Jf be ordered fields such that & is a sub-field of Jf. JT is said to be Archimedean o...
Abstract. We explore the distinction between convergence and absolute con-vergence of series in both...
In this paper the main results are :Proofs that the ordinal real numbers are real closed fields and ...
In this paper the main results are :Proofs that the ordinal real numbers are real closed fields and ...
Nested intervals and completeness are investigated in infinitesimal extensions of ordered sets
The Dedekind cuts in an ordered set form a set in the sense of constructive Zermelo-Fraenkel set the...
This work aims to show the existence and Uniqueness of the field of Real Numbers, using for this, D...