Dedekind

Beyond just calling Dedekind's approach set-theoretic, infinitary, and non-constructive, the structuralist methodology that informs it can now be analyzed as consisting of three main parts.

Dedekind's Contributions to the Foundations of Mathematics Reck, Erich 2008

However, these notions are equivalent for Dedekind domains; that is, a Dedekind domain

Citizendium, the Citizens' Compendium - Recent changes [en] 2008

I think it is better to treat random variables as we treat things like real numbers or functions: we know that there are definitions around such as Dedekind cuts or subsets of Cartesian products, but in practice we do not use these definitions and instead concentrate on various properties that are used over and over again.

Gowers's Weblog 2010

Frege's Theorem is that the five Dedekind/Peano axioms for number theory can be derived from Hume's Principle in second-order logic.

Frege's Logic, Theorem, and Foundations for Arithmetic Zalta, Edward N. 2009

Instead, we focus on the theoretical accomplishment revealed by Frege's work in Gg. Despite the failure of Basic Law V, Frege validly proved a rather deep fact about the natural numbers, namely, that the Dedekind/Peano axioms for number theory could be derived in second-order logic with the help of a single additional principle.

Frege's Logic, Theorem, and Foundations for Arithmetic Zalta, Edward N. 2009

Note the rigorous definition uses Dedekind cuts, but never mindthat.

The Volokh Conspiracy » Yow! 2009

Conceptual vs. computational approaches in algebraic number theory (Dedekind vs. Kronecker) structural vs intuitive styles in algebraic geometry (German school vs. Italian school)

Mathematical Style Mancosu, Paolo 2009

In Brouwer's vision, the mathematical continuum is indeed “constructed”, not, however, by initially shattering, as did Cantor and Dedekind, an intuitive continuum into isolated points, but rather by assembling it from a complex of continually changing overlapping parts.

Hermann Weyl Bell, John L. 2009

In the 1890s Schröder and Dedekind constructed models of the axioms of lattice theory to show that the distributive law did not follow.

The Algebra of Logic Tradition Burris, Stanley 2009

Dedekind, Richard contributions to the foundations of mathematics (Erich Reck) defaults in semantics and pragmatics (K.M. Jaszczolt) definitions (Anil Gupta)

Table of Contents 2009