Genericity versus inheritance

Quasi-stability versus Genericity

Quasi-stable ideals appear as leading ideals in the theory of Pommaret bases. We show that quasi-stable leading ideals share many of the properties of the generic initial ideal. In contrast to genericity, quasistability is a characteristic independent property that can be effectively verified. We also relate Pommaret bases to some invariants associated with local cohomology, exhibit the existen...

Feature inheritance versus extended projections

This article will show that the empirical data that Chomsky (2008) provides in favor of feature inheritance and parallel movement are rather suspect, and that there are both empirical and conceptual reasons to reject this implementation of the idea that the formal features in C and T originate in a single head position. This does not imply, however, that the latter idea should be completely rej...

Targeting the Java Virtual Machine with Genericity, Multiple Inheritance, Assertions and Expanded Types

Cosets and genericity

In a connected group of finite Morley rank in which the generic element belongs to a connected nilpotent subgroup, proper normalizing cosets of definable subgroups are not generous. We explain why this is true and what consequences this has on an abstract theory of Weyl groups in groups of finite Morley rank. The only known infinite simple groups of finite Morley rank are the simple algebraic g...

Outer models and genericity

1. Introduction Why is forcing the only known method for constructing outer models of set theory? If V is a standard transitive model of ZFC, then a standard transitive model W of ZFC is an outer model of V if V ⊆ W and V ∩ OR = W ∩ OR. Is every outer model of a given model a generic extension? At one point Solovay conjectured that if 0 # exists, then every real that does not construct 0 # lies...