SOME LOCAL EQUIVALENCE PRESERVING TRANSFORMATIONS

EXAMPLE II-4 SOME LOCAL EQUIVALENCE PRESERVING TRANSFORMATIONS... 

Now let us see some of the implications of these undecidability results. Perhaps the most important is that neither " P strongly equivalent to Q " nor " P is not strongly equivalent to Q " is partially decidable. This is why we could claim as we did that there is no point in giving a large list of elementary equivalence preserving transformations - either global or local - since no such list could be complete and result in ultimately establishing all possible equivalences. 

We shall be particularly concerned with transformations on schemes which preserve strong equivalence. Some of these will be global transformations acting cn the scheme as a unit and others will be local, replacing parts of a scheme with other strongly equivalent subschemes. 

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