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Enabling conditions for interpolated rings

Author Fred Richman



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DagSemProc.05021.12.pdf
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Fred Richman

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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

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.
Keywords
  • Brouwerian example
  • interpolated ring
  • intuitionistic algebra

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