2016Bulletin of the Belgian Mathematical Society - Simon StevinOpen access

Structures Associated with Real Closed Fields and the Axiom of Choice

Merlin Carl

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Abstract

An integer part $I$ of a real closed field $K$ is a discretely ordered subring of $K$ with minimal positive element $1$ such that, for every $x\in K$, there is $i\in I$ with $i\leq x

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An integer part $I$ of a real closed field $K$ is a discretely ordered subring of $K$ with minimal positive element $1$ such that, for every $x\in K$, there is $i\in I$ with $i\leq x

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Available abstract

An integer part $I$ of a real closed field $K$ is a discretely ordered subring of $K$ with minimal positive element $1$ such that, for every $x\in K$, there is $i\in I$ with $i\leq x

Key concepts: Mathematics, Integer (computer science), Axiom, Subring, Undecidable problem, Discrete mathematics, Field (mathematics), Axiom of choice

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