Enabling conditions for interpolated rings

Richman, Fred

doi:10.4230/DagSemProc.05021.12

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Enabling conditions for interpolated rings

Author Fred Richman

Part of: Volume: Dagstuhl Seminar Proceedings, Volume 5021
Part of: Series: Dagstuhl Seminar Proceedings (DagSemProc)
License: Creative Commons Attribution 4.0 International license
Publication Date: 2006-01-16

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DagSemProc.05021.12.pdf

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Document Identifiers

DOI: 10.4230/DagSemProc.05021.12
URN: urn:nbn:de:0030-drops-2792

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Keywords

Brouwerian example
interpolated ring
intuitionistic algebra

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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) https://doi.org/10.4230/DagSemProc.05021.12

Author Details

Fred Richman

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