Geodesic
Invariant properties of systems of formulas of elementary axiomatic
Izvestiya. Mathematics , Tome 4 (1970) no. 5, pp. 965-978.

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Under a natural definition of the properties indicated in the title, we prove the undecidability of any such properties in the case of sufficiently powerful elementary theories. In terms of invariant properties we shall formulate a general proposition which has as corollaries various results about realizable and deductively valid disjunctions of predicate formulas. 
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M. M. Kipnis. Invariant properties of systems of formulas of elementary axiomatic. Izvestiya. Mathematics , Tome 4 (1970) no. 5, pp. 965-978. http://geodesic.mathdoc.fr/item/IM2_1970_4_5_a0/

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