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Zermelo–Fraenkel set theory

Known as: Zermelo-Fraenkel axiomatization, Zermelo–Fraenkel framework, Zermelo-Fraenkel set theory 
In mathematics, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is one of several axiomatic systems that… (More)
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1969-2017
020406019692017

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Z notation

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1936-2018
19401960198020002020
Zermelo–Fraenkel set theory
Entity
Quantifier
Set theory
Occam's razor
Axiomatic system

Papers overview

Semantic Scholar uses AI to extract papers important to this topic.
2014
2014
Constructive Zermelo-Fraenkel set theory and the limited principle of omniscience
In recent years the question of whether adding the limited principle of omniscience, LPO, to constructive Zermelo-Fraenkel set… (More)
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2014
2014
Lifting Proof Theory to the Countable Ordinals: Zermelo-Fraenkel Set Theory
We describe the countable ordinals in terms of iterations of Mostowski collapsings. This gives a proof-theoretic bound on… (More)
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2012
2012
Lifschitz realizability for intuitionistic Zermelo-Fraenkel set theory
A variant of realizability for Heyting arithmetic which validates Church’s thesis with uniqueness condition, but not the general… (More)
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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… (More)
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2006
2006
An automated prover for Zermelo-Fraenkel set theory in Theorema
This paper presents some fundamental aspects of the design and the implementation of an automated prover for Zermelo-Fraenkel set… (More)
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2005
2005
Replacement versus collection and related topics in constructive Zermelo-Fraenkel set theory
While it is known that intuitionistic ZF set theory formulated with Replacement, IZFR, does not prove Collection it is a… (More)
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2005
2005
The disjunction and related properties for constructive Zermelo-Fraenkel set theory
This paper proves that the disjunction property, the numerical existence property, Church’s rule, and several other… (More)
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2004
2004
Realizability for Constructive Zermelo-Fraenkel Set Theory
Constructive Zermelo-Fraenkel Set Theory, CZF, has emerged as a standard reference theory that relates to constructive… (More)
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Highly Cited
2001
Highly Cited
2001
Typed lambda-calculus in classical Zermelo-Frænkel set theory
In this paper, we develop a system of typed lambda-calculus for the Zermelo-Frænkel set theory, in the framework of classical… (More)
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1996
1996
A linear conservative extension of Zermelo-Fraenkel set theory
In this paper, we develop the system LZF of set theory with the unrestricted comprehension in full linear logic and show that LZF… (More)
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