caa a22 4500 38803940X CHVBK 20180307125017.0 cr unu---uuuuu 161130e199806 xx s 000 0 eng 10.2307/2586845 doi S0022481200015036 pii (NATIONALLICENCE)cambridge-10.2307/2586845 There are many almost strongly minimal generalized n-gons that do not interpret an infinite group [Elektronische Daten] Generalized n-gons are certain geometric structures (incidence geometries) that generalize the concept of projective planes (the nontrivial generalized 3-gons are exactly the projective planes). In a simplified world, every generalized n-gon of finite Morley rank would be an algebraic one, i.e., one of the three families described in [9] for example. To our horror, John Baldwin [2], using methods discovered by Hrushovski [7], constructed ℵ1-categorical projective planes which are not algebraic. The projective planes that Baldwin constructed fail to be algebraic in a dramatic way. Indeed, every algebraic projective plane over an algebraically closed field is Desarguesian [12]. In particular, an algebraically closed field (isomorphic to the base field) can be interpreted in every one of them. However, in the projective planes that Baldwin constructed, one cannot even interpret an infinite group. In this article we show that the same phenomenon occurs for the generalized n-gons if n ≥ 3 is an odd integer. For each such n we construct many nonisomorphic generalized n-gons of finite Morley rank that do not interpret an infinite group. As one may expect, our method is inspired by Hrushovski and Baldwin, and we follow Baldwin's line of approach. Quite often our proofs are a verification of the fact that the proofs of Baldwin [2] for n = 3 carry over to an arbitrary positive odd integer n (which is sometimes far from being obvious). As in [2], we begin by defining a certain collection of finite graphs K* and a binary relation ≤ on these graphs. We show that (K*, ≤) satisfies the amalgamation property. Copyright © Association for Symbolic Logic 1998 Debonis Mark J. Department of Mathematics, University of California, Irvine, CA 92717, USA Nesin Ali Department of Mathematics, University of California, Irvine, CA 92717, USA The Journal of Symbolic Logic Cambridge University Press 63/2(1998-06), 485-508 0022-4812 63:2<485 1998 63 JSL https://doi.org/10.2307/2586845 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.2307/2586845 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Debonis Mark J. Department of Mathematics, University of California, Irvine, CA 92717, USA NATIONALLICENCE 700 1- Nesin Ali Department of Mathematics, University of California, Irvine, CA 92717, USA NATIONALLICENCE 773 0- The Journal of Symbolic Logic Cambridge University Press 63/2(1998-06), 485-508 0022-4812 63:2<485 1998 63 JSL CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge