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Zermelo–Fraenkel set theory

Known as: Zermelo-Fraenkel axiomatization, Zermelo–Fraenkel framework, ZFC (disambiguation) 
In mathematics, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is one of several axiomatic systems that… 
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Atomic formulaAxiomatic systemBounded quantifierBusy beaver
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Z notation

Papers overview

Semantic Scholar uses AI to extract papers important to this topic.
Highly Cited
2013
Highly Cited
2013
Energy and Spectral Efficiency of Very Large Multiuser MIMO Systems
A multiplicity of autonomous terminals simultaneously transmits data streams to a compact array of antennas. The array uses… 
2011
2011
FUNDAMENTALS OF ZERMELO-FRAENKEL SET THEORY
This paper sets out to explore the basics of Zermelo-Fraenkel (ZF) set theory without choice. We will take the axioms (excluding… 
2007
2007
Realizability for Constructive Zermelo-Fraenkel Set Theory
Constructive Zermelo-Fraenkel Set Theory, CZF, has emerged as a standard reference theory that relates to constructive… 
2005
2005
The disjunction and related properties for constructive Zermelo-Fraenkel set theory
  • M. Rathjen
  • Journal of Symbolic Logic
  • 2005
  • Corpus ID: 12117179
Abstract This paper proves that the disjunction property, the numerical existence property. Church's rule, and several other… 
2003
2003
Puzzle: Zermelo-Fraenkel set theory is inconsistent
In this note, we present a puzzle. We prove that Zermelo-Fraenkel set theory is inconsistent by proving, using Zermelo-Fraenkel… 
Highly Cited
2001
Highly Cited
2001
Typed lambda-calculus in classical Zermelo-Frænkel set theory
system of simple types, which uses the intuitionistic propositional calculus, with the only connective →. It is very important… 
1999
1999
Models of Second-Order Zermelo Set Theory
  • G. Uzquiano
  • Bulletin of Symbolic Logic
  • 1999
  • Corpus ID: 10138274
In [12], Ernst Zermelo described a succession of models for the axioms of set theory as initial segments of a cumulative… 
1985
1985
Global Quantification in Zermelo-Fraenkel Set Theory
My aim here is to investigate the role of global quantifiers—quantifiers ranging over the entire universe of sets—in the… 
Highly Cited
1977
Highly Cited
1977
Internal set theory: A new approach to nonstandard analysis
1. Internal set theory. We present here a new approach to Abraham Robinson's nonstandard analysis [10] with the aim of making… 
1968
1968
Zermelo-Fraenkel set theory
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