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Yemon Choi
Yemon Choi
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Let $X$X be your favorite undecidable set of primes. In a language with one unary function symbol, say f^p(x) = x iff $p$p is in $X$X and also that there is a unique cycle of length $p$p. Add that f is a bijection. Now the prime model contains cycles of exactly the lengths in $X$X and the theory is undecidable. But it is categorical in all uncountable power and therefore omega stable.

Let $X$ be your favorite undecidable set of primes. In a language with one unary function symbol, say f^p(x) = x iff $p$ is in $X$ and also that there is a unique cycle of length $p$. Add that f is a bijection. Now the prime model contains cycles of exactly the lengths in $X$ and the theory is undecidable. But it is categorical in all uncountable power and therefore omega stable.

Let X be your favorite undecidable set of primes. In a language with one unary function symbol, say f^p(x) = x iff p is in X and also that there is a unique cycle of length p. Add that f is a bijection. Now the prime model contains cycles of exactly the lengths in X and the theory is undecidable. But it is categorical in all uncountable power and therefore omega stable.

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edit approved Sep 8, 2014 at 15:09
Mostafa Mirabi
edit approved Sep 8, 2014 at 15:09
Mostafa Mirabi
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Let X$X$ be your favorite undecidable set of primes. In a language with one unary function symbol, say f^p(x) = x iff p$p$ is in X$X$ and also that there is a unique cycle of length p$p$. Add that f is a bijection. Now the prime model contains cycles of exactly the lengths in X$X$ and the theory is undecidable. But it is categorical in all uncountable power and therefore omega stable.

Let X be your favorite undecidable set of primes. In a language with one unary function symbol, say f^p(x) = x iff p is in X and also that there is a unique cycle of length p. Add that f is a bijection. Now the prime model contains cycles of exactly the lengths in X and the theory is undecidable. But it is categorical in all uncountable power and therefore omega stable.

Let $X$ be your favorite undecidable set of primes. In a language with one unary function symbol, say f^p(x) = x iff $p$ is in $X$ and also that there is a unique cycle of length $p$. Add that f is a bijection. Now the prime model contains cycles of exactly the lengths in $X$ and the theory is undecidable. But it is categorical in all uncountable power and therefore omega stable.

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John Baldwin
John Baldwin
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Let X be your favorite undecidable set of primes. In a language with one unary function symbol, say f^p(x) = x iff p is in X and also that there is a unique cycle of length p. Add that f is a bijection. Now the prime model contains cycles of exactly the lengths in X and the theory is undecidable. But it is categorical in all uncountable power and therefore omega stable.