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Full satisfaction classes, definability, and automorphisms
[article]
2021
arXiv
pre-print
We show that for every countable recursively saturated model M of Peano Arithmetic and every subset A ⊆ M, there exists a full satisfaction class S_A ⊂ M^2 such that A is definable in (M,S_A) without parametres. It follows that in every such model, there exists a full satisfaction class which makes every element definable and thus the expanded model is minimal and rigid. On the other hand, we show that for every full satisfaction class S there are two elements which have the same arithmetical
arXiv:2104.09969v1
fatcat:mnoaudy3yzbf7oxd67pnqtunma