Dave Marker
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Registered User
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May 5 |
awarded | ● Yearling |
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Apr 13 |
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Surreals and NSA: some foundational issues Barwise and Schlipf showed that the same holds if $M$ is recursively saturated and $T$ is recursively axiomatizable. |
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Apr 13 |
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Surreals and NSA: some foundational issues Let $M$ be a saturated model and $T$ a theory in a expanded language that is consistent with the theory of $M$. Then there you can interpret the new symbols in $M$ so that $M$ is a model of $T$. (Exercise 4.5.35 in my book.) Let $T_0$ be a consistent extension of Open Induction. Let $R$ be a saturated RCF. Add a predicate symbol $P$ and let $T$ be the theory saying that $P$ is a model of $T$ and every element of $R$ has an integer part in $P$. This is consistent with RCF since it's true in the real closure of a model of $T_0$. So there is $P\subset R$, $(R,P)\models T$. |
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Apr 11 |
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Surreals and NSA: some foundational issues @Joel, for a start the square root of 2 is rational! |
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Apr 8 |
answered | dense orders are saturated |
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Feb 8 |
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Is there any o-minimal expansion of the real field with functions of growth higher than exponential? By contrast, one might also ask if there are o-minimal expansions where you have functions that grow faster than polynomials but no functions of exponential growth. A beautiful and surprising theorem of Chris Miller showed that you can't. Indeed exponentiation is definable in any o-minimal expansion of the reals containing any function of super-polynomial growth. |
