By Cvitanovic P.

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**Additional info for Group theory (Lie and other) (draft 2002)**

**Sample text**

We now have all the tools to express the LCA. We will approach the de®nition of the LCA step by step, keeping in mind that this axiom interlocks nonterminal and terminal nodes. As a ®rst step, let us consider the LCA from an informal point of view: ``The intuition that I would like to pursue is that there should be a very close match between the linear ordering relation on the set of terminals and some comparable relation on nonterminals. By comparable, I now mean locally linear'' (Kayne 1994, 5).

In any way `by no means' Let us start by assuming that the complement of a believe-type verb is indeed a small clause. Adverbial elements like the one in (18) can occur between the subject and the predicate of a small clause like the one in (17). (19) Gianni non ritiene [queste foto [in alcun modo] la causa Gianni not considers these pictures in any way the cause della rivolta]. of-the riot This suggests that the structure that is the complement of the believe-type verb is not a ``bare'' small clause like the small clauses found in copular sentences, but a richer construction involving at least one functional projection.

Thus, inverse copular constructions do not necessarily refute the morphological theory of movement. Indeed, one possibility would be to say they are exceptions, and to maintain the morphological theory of movement. Simply, I will not pursue this line of reasoning; instead, I assume that there are good empirical reasons to generalize the alternative proposal based on a weak version of antisymmetry to other, possibly all, cases of movement. Indirect support for this choice is suggested in the Sources of Symmetry 49 appendix, where the pervasive presence of ``inverse'' constructions in syntax is illustrated synthetically.