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Blake Manner wrote:
> Is it true that for any two elements of some L-structure A realizing
> the same complete type, there is an automorphism of A swapping those
> two elements, and fixing all the rest of A?
this seems almost immediate
the automoprhisms are those f:A->A
that preserve all definable relations
the complete types are those collections
of definable relations
maximal over the formulae on its elements
so
if two elements realise the same complete type
all definable relations between those elements
and the rest of the structure
do not differ
and the swap mapping is automorphic
am i missing a technicality?
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galathaea: prankster, fablist, magician, liar
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