The Abstract Lace Expansion
نویسندگان
چکیده
LACES DEFINITION. Let P be a finite set of properties. A mapping l that Ž . assigns to any subset S ; P another subset l S is called a lace map if, for all S, G, S , S ; P: 1 2 Ž . Ž . i l S ; S; Ž . Ž . Ž . Ž . ii l S ; G ; S « l G s l S ; Ž . Ž . Ž . Ž . Ž . iii l S s l S « l S j S s l S . 1 2 1 2 1 Ž . Ž . Ž . A set L for which l L s L is called a lace. By applying ii to G s l S , Ž Ž .. Ž . Ž . it is seen that l l S s l S , for any set of properties S; hence l S is always a lace and l is a projection, l 2 s l. Ž . Ž . If L is a lace, then, by iii , there exists a set C L ; P _ L such that
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The abstract lace expansion
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