Difference between revisions of "Integer parts of real closed fields"
From Peano's Parlour
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== Tennenbaum property == | == Tennenbaum property == | ||
| − | Je\v{z}\'abek and Ko{\l}odziejczyk show <cite> jezabekkolodziejczyk2013:real < | + | Je\v{z}\'abek and Ko{\l}odziejczyk show <cite> jezabekkolodziejczyk2013:real </cite> that if $A$ is a model of Open Induction and the real closure of $A$ is recursively saturated, then $+^A$ and $\leq^A$ cannot be both recursive, and they ask whether it is true that if every unbounded real closed field with |
an integer part satisfying an arithmetic theory $T$ is recursively saturated, then $T$ has no recursive | an integer part satisfying an arithmetic theory $T$ is recursively saturated, then $T$ has no recursive | ||
nonstandard models. | nonstandard models. | ||
Revision as of 06:00, 20 June 2013
Tennenbaum property
Je\v{z}\'abek and Ko{\l}odziejczyk show [1] that if $A$ is a model of Open Induction and the real closure of $A$ is recursively saturated, then $+^A$ and $\leq^A$ cannot be both recursive, and they ask whether it is true that if every unbounded real closed field with an integer part satisfying an arithmetic theory $T$ is recursively saturated, then $T$ has no recursive nonstandard models.
