Substantive equality revisited

Equality, Revisited

In 1979 Yao published a paper that started the field of communication complexity and asked, in particular, what was the randomised complexity of the Equality function (EQ) in the Simultaneous Message Passing (SMP) model (for the question to be non-trivial, one must consider the setting of private randomness). The tight lower bound Ω( √ n) was given only in 1996 by Newman and Szegedy. In this wo...

Deep Equality Revisited

We revisit the notion of deep equality among objects in an ob ject database from a formal point of view We present three natural formalizations of deep equality one based on the in nite value trees associated with objects one based on the greatest xpoint of an oper ator on equivalence relations among objects and one based on indis tinguishability of objects using observations of atomic values r...

Relation Formulas for Protoalgebraic Equality Free Quasivarieties; Pałasińska's Theorem Revisited

We provide a new proof of the following Pa lasińska’s theorem: Every finitely generated protoalgebraic relation distributive equality free quasivariety is finitely axiomatizable. The main tool we use are Q-relation formulas, for a protoalgebraic equality free quasivariety Q, which are the counterparts of the congruence formulas used for describing the generation of congruences in algebras. Havi...

Equality of bulk and edge Hall conductance revisited

The integral quantum Hall effect can be explained either as resulting from bulk or edge currents (or, as it occurs in real samples, as a combination of both). This leads to different definitions of Hall conductance, which agree under appropriate hypotheses, as shown by Schulz-Baldes et al. by means of K-theory. We propose an alternative proof based on a generalization of the index of a pair of ...

Religion, Politics and Gender Equality Public Religions Revisited