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Enabling conditions for interpolated rings

Authors: Fred Richman

Published in: Dagstuhl Seminar Proceedings, Volume 5021, Mathematics, Algorithms, Proofs (2006)


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.

Cite as

Fred Richman. Enabling conditions for interpolated rings. In Mathematics, Algorithms, Proofs. Dagstuhl Seminar Proceedings, Volume 5021, pp. 1-7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)


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@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-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.05021.12},
  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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