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Revision as of 20:54, 15 November 2012
, 20:54, 15 November 2012→6.31. Relations in General: markup
Any property <math>P\!</math> of <math>L_{x \,\text{at}\, j}\!</math> constitutes a ''local incidence property'' of <math>L\!</math> with reference to the locus <math>x \,\text{at}\, j.\!</math>
Any property <math>P\!</math> of <math>L_{x \,\text{at}\, j}\!</math> constitutes a ''local incidence property'' of <math>L\!</math> with reference to the locus <math>x \,\text{at}\, j.\!</math>
'''Definition.''' A <math>k\!</math>-place relation <math>L \subseteq X_1 \times \ldots \times X_k\!</math> is ''<math>P\!</math>-regular at <math>j\!</math>'' if and only if every flag of <math>L\!</math> with <math>x\!</math> at <math>j\!</math> is <math>P,\!</math> letting <math>x\!</math> range over the domain <math>X_j,\!</math> in symbols, if and only if <math>P(L_{x \,\text{at}\, j})\!</math> is true for all <math>x \in X_j.\!</math>
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Of particular interest are the local incidence properties of relations that can be calculated from the cardinalities of their local flags, and these are naturally called "numerical incidence properties" (NIPs).
Of particular interest are the local incidence properties of relations that can be calculated from the cardinalities of their local flags, and these are naturally called "numerical incidence properties" (NIPs).
