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Answer by Kyle Gannon for Is $Th(\mathbb{Z}[x])$ uncountably categorical?
This is a response to Rene Schipperus's comment asking whether or not we can define an ordering on the integers in this structure. It turns out that we can. We say that $P(x)$, i.e. "x is positive",...
View ArticleAnswer by Rene Schipperus for Is $Th(\mathbb{Z}[x])$ uncountably categorical?
Since you contain the arithmetic of the integers you can pick some infinite family of primes and say that an element of degree $0$ is divisible by those primes and not any other primes. This gives...
View ArticleIs $Th(\mathbb{Z}[x])$ uncountably categorical?
Consider $T=Th(\mathbb{Z}[x])$ in the language $L = \{0,1,+,\times,deg(), \circ\}$ where $0,1,+$ and $\times$ have their usual interpretations, $deg()$ is a unary function symbol which gives the degree...
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