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2008.86: Bounded super real closed rings

2008.86: Marcus Tressl (2008) Bounded super real closed rings.

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Abstract

This note is a complement to the paper "M. Tressl, Super real closed rings", where super real closed rings are introduced and studied. A bounded super real closed ring A is a commutative unital ring A together with an operation FA:An -> A for every bounded continuous map F:ℝn -> ℝ, so that all term equalities between the F's remain valid for the FA's. We show that bounded super real closed rings are precisely the convex subrings of super real closed rings: for every bounded super real closed ring there is a largest super real closed subring B contained in A and a smallest super real closed ring C containing A. Moreover B is convex in C. The assignment A↦C is an idempotent mono-reflector from bounded to arbitrary super real closed rings which allows to transfer many of the algebraic results from the unbounded to the bounded situation

Item Type:MIMS Preprint
Uncontrolled Keywords:real closed rings, rings of continuous functions, model theory
Subjects:MSC 2000 > 03 Mathematical logic and foundations
MSC 2000 > 46 Functional analysis
MIMS number:2008.86
Deposited By:Dr Marcus Tressl
Deposited On:10 October 2008

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