𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Non-constructive Properties of the Real Numbers

✍ Scribed by Paul Howard; Kyriakos Keremedis; Jean E. Rubin; Adrienne Stanley; Eleftherios Tatchtsis

Publisher
John Wiley and Sons
Year
2001
Tongue
English
Weight
159 KB
Volume
47
Category
Article
ISSN
0044-3050

No coin nor oath required. For personal study only.

πŸ“œ SIMILAR VOLUMES

The Arithmetical Hierarchy of Real Numbe
The Arithmetical Hierarchy of Real Numbers
✍ Xizhong Zheng; Klaus Weihrauch πŸ“‚ Article πŸ“… 2001 πŸ› John Wiley and Sons 🌐 English βš– 225 KB πŸ‘ 1 views
A note on the axiomatisation of real num
A note on the axiomatisation of real numbers
✍ Thierry Coquand; L. Henri Lombardi πŸ“‚ Article πŸ“… 2008 πŸ› John Wiley and Sons 🌐 English βš– 86 KB πŸ‘ 2 views

## Abstract Is it possible to give an abstract characterisation of constructive real numbers? A condition should be that all axioms are valid for Dedekind reals in any topos, or for constructive reals in Bishop mathematics. We present here a possible first‐order axiomatisation of real numbers, whic

On the Pythagoras Numbers of Real Analyt
On the Pythagoras Numbers of Real Analytic Rings
✍ JosΓ© F Fernando πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 155 KB

We show that the Pythagoras number of a real analytic ring of dimension 2 is finite, bounded by a function of the multiplicity and the codimension.

On the Cauchy completeness of the constr
On the Cauchy completeness of the constructive Cauchy reals
✍ Robert S. Lubarsky πŸ“‚ Article πŸ“… 2007 πŸ› John Wiley and Sons 🌐 English βš– 200 KB

## Abstract It is consistent with constructive set theory (without Countable Choice, clearly) that the Cauchy reals (equivalence classes of Cauchy sequences of rationals) are not Cauchy complete. Related results are also shown, such as that a Cauchy sequence of rationals may not have a modulus of c