This result follows straight from the geometric properties of þ-forking and it is nowhere near the independence theorem (which we will call “independent amalgamation”) one has in simple theories. In [?], Kim proved that the only independence relation satisfying symmetry, local character, transitivity and the independence theorem was forking in a simple theory; since there are well known example...

The first part of this paper provides a comprehensive and self-contained account of the interrelationships between algebraic properties of varieties and properties of their free algebras and equational consequence relations. In particular, proofs are given of known equivalences between the amalgamation property and the Robinson property, the congruence extension property and the extension prope...

We present definitions of homology groups Hn(p), n ≥ 0, associated to a complete type p. We show that if the generalized amalgamation properties hold, then the homology groups are trivial. We compute the group H2(p) for strong types in stable theories and show that any profinite abelian group can occur as the group H2(p). The work described in this paper was originally inspired by Hrushovski’s ...

The aim of this paper is to present a detailed explanation of three models of Shelah. We show the rule of the amalgamation in the construction of models in which all deenable sets of reals have Baire property or are Lebesgue measurable. Next we construct a model in which every projective set of reals has Baire property, a model with the Uniformization Property and a model of ZF + DC in which al...

The center-of-mass(CM) of a few-body quantum system with a central field is discussed. If the particles are in the designative eigenstates, the CM coordinates of the system can be well-defined. In the CM bag model as well as in other models with central fields, the CM-freedom separation rule and effective nucleon electro-magnetic currents can be presented without any undetermined parameter.