5 citations · 8 across the 10 of their papers we have counts for
10 papers
There are more non-Cantorian sets than are Cantorian
Zuhair Al-Johar
When working in NF, [1] there is a sense that there are more non-Cantorian sets than Cantorian sets. But it is not that immediate result as one expects, since they are externally e…
Set Theory is interpretable in Class Ordering Theory
Zuhair Al-Johar
Here it is shown that standard set theory can be interpreted in a theory about order. The ordering here is about non-extensional flat classes, i.e. classes that are not elements of…
An alternative proof of Godel's first incompleteness theorem
Zuhair A. Al-Johar
This proof of Godel's first incompleteness theorem doesn't require omega-consistency, nor does it refer to codes of negated sentences as in Rosser's. It begins from where Godel's u…
Towards an untyped proof of Con(NF)
Zuhair Al-Johar
The idea of this approach towards proving the consistency of Quine's New Foundations set theory is to go in a completely untyped manner. So no contemplation about types is utilized…
Invariance under permutations as a semantic motivation for Stratification
Zuhair Al-Johar
This article examines the notion of invariance under different kinds of permutations in a milieu of a theory of classes and sets, as a semantic motivation for Quine's new foundatio…
Acyclic Comprehension is equal to Stratified Comprehension
Zuhair Al-Johar, M. Randall Holmes
A new criterion of comprehension is defined, initially termed by myself as "connected" and finally as "Acyclic" by Mr. Randall Holmes. Acyclic comprehension simply asserts that for…
ZF*-Extensionality interprets full ZF
Zuhair Al-Johar
Dana Scott had shown that removing Extensionality from ZF set theory formalized in the customary manner would weaken it down to Zermelo set theory. The following proof is my person…
Stratified formulas are equivalent to Acyclic formulas: A review
Zuhair Al-Johar
This document include my comments on Nathan Bowler's proof that every stratified formula is equivalent to an acyclic formula. The whole proof of Nathan's is quoted exactly as it's…
Labeled Mereological Set Theory
Zuhair Al-Johar
The methodology used here might provide a neat method of examining paradoxes and ways to circumvent them. Most of the known set theoretic paradoxes (Russell's, Cantor's, Burali-For…
Short Axiomatization of Stratified Comprehension
Zuhair A. Al-Johar
Several finite axiomatizations of stratified comprehension are known. This paper gives five set existence principles which, in the presence of Extensionality, yield the fourteen se…