Algebraic relations and presentations

On Presentations of Algebraic Structures

Algebraic Presentations of Dependent Type Theories

In this paper, we propose an abstract definition of dependent type theories as essentially algebraic theories. One of the main advantages of this definition is its composability: simple theories can be combined into more complex ones, and different properties of the resulting theory may be deduced from properties of the basic ones. We define a category of algebraic dependent type theories which...

Algebraic Relations Involving Relative Risk

Epidemiologists have long regarded relative risk (RR) as a key measure of association between two binary variables. Yet even when the sample is representative of the population, associations having a RR > 9 may have a relatively small value for Phi (φ < .3). This paper provides additional reasons for using RR instead of φ. (1) Formulas relating φ and RR are derived. A relative φ is constructed;...

Equivalence Relations in Algebraic Geometry

1. The cycle groups C8. An algebraic variety F i n w-dimensional complex projective space P ( n ) is obtained by equating to zero a finite number of forms Fi(x0, • • • , xn)f • • • , Fm(xo, • • • , xn) with complex coefficients ; F is assumed to be nonempty. If F i s irreducible, that is, if V is not the union of a finite number of proper subvarieties, it is possible to associate with V in seve...

Algebraic Relations for Recursive Sequences

Through the following, we establish the conditions which allow us to express recursive sequences of real numbers, enumerated through the recurrence relation an+1 = Aan + Ban−1, by means of algebraic equations in two variables of degree n ∈ N . We do this, as far as we know, like it has never been formalized before. I’d like to precise that the work was develop without the support of any well-kn...