Ternary scale theorems: Difference between revisions

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 ==== Statement (3) ====
-For (3), we now only need to see that if len(''S'') is odd and ''S'' is SGA, ''S'' is abstractly SV3. But the argument in case 2 above works when you substitute any odd-step interval classes in ''S'' instead of a 1-step (abstract SV3 wasn't used). To get even-step interval classes, we can take octave complements. Hence any interval class in such a scale comes in (abstractly) exactly 3 sizes.
+We only need to see that if len(''S'') is odd and ''S'' is SGA, ''S'' is abstractly SV3. But the argument in case 2 above works when you substitute any odd-step interval classes in ''S'' instead of a 1-step (abstract SV3 wasn't used). To get even-step interval classes, we can take octave complements. Hence any interval class in such a scale comes in (abstractly) exactly 3 sizes.
 ==== Statement (4) ====