  In this paper we briefly summarize the contents of Manzonetto's PhD thesis
which concerns denotational semantics and equational/order theories of the pure
untyped lambda-calculus. The main research achievements include: (i) a general
construction of lambda-models from reflexive objects in (possibly
non-well-pointed) categories; (ii) a Stone-style representation theorem for
combinatory algebras; (iii) a proof that no effective lambda-model can have
lambda-beta or lambda-beta-eta as its equational theory (this can be seen as a
partial answer to an open problem introduced by Honsell-Ronchi Della Rocca in
1984).
