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Enabling conditions for interpolated rings Richman, Fred Brouwerian example interpolated ring intuitionistic algebra 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Fred Richman 2006 Is Part Of Dagstuhl Seminar Proceedings, Volume 5021, Mathematics, Algorithms, Proofs (2006) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagSemProc.05021.12 urn:nbn:de:0030-drops-2792 https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05021.12 eng https://creativecommons.org/licenses/by/4.0/legalcode