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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.

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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.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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Enabling conditions for interpolated rings

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