Varieties of combinatorial geometries
نویسندگان
چکیده
منابع مشابه
Varieties of Combinatorial Geometries
A hereditary class of (finite combinatorial) geometries is a collection of geometries which is closed under taking minors and direct sums. A sequence of universal models for a hereditary class 'S of geometries is a sequence (T„ ) of geometries in ?T with rank Tn = n, and satisfying the universal property: if G is a geometry in 5" of rank n, then G is a subgeometry of T„. A variety of geometries...
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Quasiminimality In this chapter we introduce Zilber’s notion [Zil05] of an abstract quasiminimalexcellent class and prove Theorem 2.23: Lω1,ω-definable quasiminimal-excellent classes satisfying the countable closure condition are categorical in all powers. In the next chapter we expound Zilber’s simplest concrete algebraic example. In Chapter 25, we will place this example in the context of She...
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R. Stanley, in an investigation of modular flats in geometries (Algebra Universalis 1-2 (1971), 214—217), proved that the characteristic polynomial xW of a modular flat x divides the characteristic polynomial x(G) of a geometry G. In this paper we identify the quotient: THEOREM. // x is a modular flat of G, x(G)/x(x) = X(7^(G))/(\ 1), where TX{G) is the complete Brown truncation of G by x. (The...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1982
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1982-0654846-9