1 Unique Undefinable Elements
نویسنده
چکیده
[Fu68] presents structures, in a finite relational type, with unique undefinable elements and recursive theories. We present somewhat simpler examples, with somewhat stronger properties. We also present structures, in a finite relational type, whose unique undefinable element is weak second order undefinable. We convert all examples of a similar nature to corresponding examples in the form of bipartite graphs and atomic inclusions. We show that "there is a structure, in a finite relational type, with a unique second order undefinable element" is not provable in ZFC (assuming ZFC is consistent). We explore some properties of structures with unique undefinable elements.
منابع مشابه
Unique Undefinable Elements
We present a structure (in a finite relational type) with a unique undefinable element. Furthermore, the unique undefinable element is undefinable even if we use the quantifier "there exist infinitely many" and quantitative variants. We show that the structures can be taken to be a graph. We also prove that "there is a structure (in a finite relational type) with a unique second order undefinab...
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