Nonstandard foundations of equilibrium search models

Linearly Stratified Models for the Foundations of Nonstandard Mathematics

Assuming the existence of an inaccessible cardinal, transitive full models of the whole set theory, equipped with a linearly-valued rank function, are constructed. Such models generalize superstructures and provide a global framework for nonstandard mathematics. MSClassification: 03H05, 03C20.

FOUNDATIONS OF NONSTANDARD ANALYSIS A Gentle Introduction to Nonstandard Extensions

On the game-theoretic foundations of competitive search equilibrium

We provide a unified directed search framework with general production and matching specifications that encompasses most of the existing literature. We prove the existence of subgame perfect Nash equilibria in pure firm strategies in a finite version of the model. We use this result to derive a more complete characterization of the equilibrium set for the finite economy and to extend convergenc...

On the Foundations of Nonstandard Mathematics

In this paper we survey various set-theoretic approaches that have been proposed over the last thirty years as foundational frameworks for the use of nonstandard methods in mathematics. Introduction. Since the early developments of calculus, infinitely small and infinitely large numbers have been the object of constant interest and great controversy in the history of mathematics. In fact, while...

Foundations of Fuzzy Sets: a Nonstandard Approach

The well known results on the inner limitations of classical mathematics (L6wenheim-Skolem Theorems, and G6del's Theorems) and the introduction of a host of new set-like concepts, indicate the presence of something which is beyond the grasp of Cantorian set theory. In different ways each limitation expresses a basic uncertainty in Mathematics. GOdel's Theorems essentially express the following:...