How Gödel Transformed Set Theory, Volume 53, Number 4

How Gödel Transformed Set Theory

K urt Gödel (1906–1978), with his work on the constructible universe L, established the relative consistency of the Axiom of Choice and the Continuum Hypothesis. More broadly, he secured the cumulative hierarchy view of the universe of sets and ensured the ascendancy of first-order logic as the framework for set theory. Gödel thereby transformed set theory and launched it with structured subjec...

Gödel, Inconsistency, Provability, and Truth: An Exchange of Letters, Volume 53, Number 4

462 NOTICES OF THE AMS VOLUME 53, NUMBER 4 On the eve of Gödel’s centennial, it is distressing that his incompleteness theorems continue to be so misunderstood. The article “Whither Mathematics?”, which appeared in the December 2005 Notices, is an egregious example. On page 1350 it is stated that Gödel “established that the consistency of arithmetic was not provable”, a claim reiterated again f...

A System of Axioms of Set Theory for the Rationalists, Volume 53, Number 2

Monads and sets. On Gödel, Leibniz, and the reflection principle

Gödel once offered an argument for the general reflection principle in set theory that took the form of an analogy with Leibniz’ Monadology. I discuss the mathematical and philosophical background to Gödel’s argument, reconstruct the proposed analogy in detail, and argue that it has no justificatory force. Voor Göran, in dank en vriendschap

Reduction of DEA-Performance Factors Using Rough Set Theory: An Application of Companies in the Iranian Stock Exchange

he financial management field has witnessed significant developments in recent years to help decision makers, managers and investors, to made optimal decisions. In this regard, the institutions investment strategies and their evaluation methods continuously change with the rapid transfer of information and access to the fi- nancial data. When information is available ...