O ciałach uporządkowanych

Piotr Błaszczyk

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia (2012)

  • Volume: 4, page 15-30
  • ISSN: 2080-9751

Abstract

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In this paper, we present some basic facts concerning ordered fields. We review definitions of an ordered field, give an example of a field that admits many orderings, and present equivalent definitions of the axiom of Archimedes and the continuity axiom. We show how to extend an ordered field by means of an ultrapower construction and formal power series.

How to cite

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Piotr Błaszczyk. "O ciałach uporządkowanych." Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia 4 (2012): 15-30. <http://eudml.org/doc/296267>.

@article{PiotrBłaszczyk2012,
abstract = {In this paper, we present some basic facts concerning ordered fields. We review definitions of an ordered field, give an example of a field that admits many orderings, and present equivalent definitions of the axiom of Archimedes and the continuity axiom. We show how to extend an ordered field by means of an ultrapower construction and formal power series.},
author = {Piotr Błaszczyk},
journal = {Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia},
keywords = {ordered fields; Archimedean field; non-Archimedean field; continuity; hyperreals},
language = {pol},
pages = {15-30},
title = {O ciałach uporządkowanych},
url = {http://eudml.org/doc/296267},
volume = {4},
year = {2012},
}

TY - JOUR
AU - Piotr Błaszczyk
TI - O ciałach uporządkowanych
JO - Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
PY - 2012
VL - 4
SP - 15
EP - 30
AB - In this paper, we present some basic facts concerning ordered fields. We review definitions of an ordered field, give an example of a field that admits many orderings, and present equivalent definitions of the axiom of Archimedes and the continuity axiom. We show how to extend an ordered field by means of an ultrapower construction and formal power series.
LA - pol
KW - ordered fields; Archimedean field; non-Archimedean field; continuity; hyperreals
UR - http://eudml.org/doc/296267
ER -

References

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