Stability of representations of effective partial algebras

Mathematical Logic Quarterly 57 (2):217-231 (2011)
  Copy   BIBTEX

Abstract

An algebra is effective if its operations are computable under some numbering. When are two numberings of an effective partial algebra equivalent? For example, the computable real numbers form an effective field and two effective numberings of the field of computable reals are equivalent if the limit operator is assumed to be computable in the numberings . To answer the question for effective algebras in general, we give a general method based on an algebraic analysis of approximations by elements of a finitely generated subalgebra. Commonly, the computable elements of a topological partial algebra are derived from such a finitely generated algebra and form a countable effective partial algebra. We apply the general results about partial algebras to the recursive reals, ultrametric algebras constructed by inverse limits, and to metric algebras in general. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Other Versions

No versions found

Links

PhilArchive

    This entry is not archived by us. If you are the author and have permission from the publisher, we recommend that you archive it. Many publishers automatically grant permission to authors to archive pre-prints. By uploading a copy of your work, you will enable us to better index it, making it easier to find.

    Upload a copy of this work     Papers currently archived: 102,283

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Computable Presentations of C*-Algebras.F. O. X. Alec - 2024 - Journal of Symbolic Logic 89 (3):1313-1338.
A Real Number Structure that is Effectively Categorical.Peter Hertling - 1999 - Mathematical Logic Quarterly 45 (2):147-182.
A note on partial numberings.Serikzhan Badaev & Dieter Spreen - 2005 - Mathematical Logic Quarterly 51 (2):129-136.
Categoricity Spectra for Polymodal Algebras.Nikolay Bazhenov - 2016 - Studia Logica 104 (6):1083-1097.
Recursive unary algebras and trees.Bakhadyr Khoussainov - 1994 - Annals of Pure and Applied Logic 67 (1-3):213-268.
Extremal numberings and fixed point theorems.Marat Faizrahmanov - 2022 - Mathematical Logic Quarterly 68 (4):398-408.

Analytics

Added to PP
2013-11-03

Downloads
27 (#845,555)

6 months
2 (#1,626,901)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

No citations found.

Add more citations

References found in this work

Theorie der Numerierungen I.Ju L. Eršov - 1973 - Mathematical Logic Quarterly 19 (19‐25):289-388.
A Real Number Structure that is Effectively Categorical.Peter Hertling - 1999 - Mathematical Logic Quarterly 45 (2):147-182.
On Computable Sequences.A. Mostowski - 1960 - Journal of Symbolic Logic 25 (4):367-367.
Notation Systems and Recursive Ordered Fields.Yiannis N. Moschovakis - 1966 - Journal of Symbolic Logic 31 (4):650-651.

View all 7 references / Add more references