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When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.05021.12
URN: urn:nbn:de:0030-drops-2792
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2006/279/
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Richman, Fred
Enabling conditions for interpolated rings
Abstract
If A is a subring of a ring B, then an interpolated ring is the union of A and {b in B : P} for some proposition P. These interpolated rings come up frequently in the construction of Brouwerian examples. We study conditions on the inclusion of A in B that guarantee, for some property of rings, that if A and B both have that property, then so does any interpolated ring. Classically, no condition is necessary because each interpolated ring is either A or B. We also would like such a condition to be necessary in the sense that if it fails, and every interpolated ring has the property, then some omniscience principle holds.
BibTeX - Entry
@InProceedings{richman:DagSemProc.05021.12,
author = {Richman, Fred},
title = {{Enabling conditions for interpolated rings}},
booktitle = {Mathematics, Algorithms, Proofs},
pages = {1--7},
series = {Dagstuhl Seminar Proceedings (DagSemProc)},
ISSN = {1862-4405},
year = {2006},
volume = {5021},
editor = {Thierry Coquand and Henri Lombardi and Marie-Fran\c{c}oise Roy},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2006/279},
URN = {urn:nbn:de:0030-drops-2792},
doi = {10.4230/DagSemProc.05021.12},
annote = {Keywords: Brouwerian example, interpolated ring, intuitionistic algebra}
}
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Keywords: |
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Brouwerian example, interpolated ring, intuitionistic algebra |
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Collection: |
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05021 - Mathematics, Algorithms, Proofs |
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Issue Date: |
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2006 |
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Date of publication: |
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16.01.2006 |
