Naive Set Theory

1979 ◽  
pp. 1-34
Author(s):  
Keith J. Devlin
Keyword(s):  
Set Theory ◽  
Naive Set Theory

Naive Set Theory

2014 ◽  
pp. 1-8
Author(s):  
Ralf Schindler
Keyword(s):  
Set Theory ◽  
Naive Set Theory

Extensionality and Restriction in Naive Set Theory

Studia Logica ◽  
2010 ◽  
Vol 94 (1) ◽  
pp. 87-104 ◽  
Author(s):  
Zach Weber
Keyword(s):  
Set Theory ◽  
Naive Set Theory

An Essay on Denotational Mathematics

2019 ◽  
pp. 1629-1640
Author(s):  
Giuseppe Iurato
Keyword(s):  
Artificial Intelligence ◽  
Computer Science ◽  
Set Theory ◽  
Neuronal Networks ◽  
Theoretical Computer Science ◽  
Mathematical Framework ◽  
Theoretical Computer ◽  
Cognitive Informatics ◽  
Naive Set Theory ◽  
Software Science

Denotational mathematics is a new rigorous discipline of theoretical computer science that springs out from the attempt to provide a suitable mathematical framework in which laid out new algebraic structures formalizing certain formal patterns coming from computational and natural intelligence, software science, cognitive informatics, neuronal networks, and artificial intelligence. In this chapter, a very brief but rigorous exposition of the main formal structures of denotational mathematics is outlined within naive set theory.

CONCEPTUAL FOUNDATIONS OF OPERATIONAL SET THEORY

2010 ◽  
Vol 45 (1) ◽  
pp. 29-50
Author(s):  
Kaj Børge Hansen
Keyword(s):  
Turing Machine ◽  
Set Theory ◽  
Formation Process ◽  
Careful Analysis ◽  
Type Structure ◽  
Foundations Of Mathematics ◽  
Naive Set Theory ◽  
Suitable Combination ◽  
Conceptual Foundations

I formulate the Zermelo-Russell paradox for naive set theory. A sketch is given of Zermelo’s solution to the paradox: the cumulative type structure. A careful analysis of the set formation process shows a missing component in this solution: the necessity of an assumed imaginary jump out of an infinite universe. Thus a set is formed by a suitable combination of concrete and imaginary operations all of which can be made or assumed by a Turing machine. Some consequences are drawn from this improved analysis of the concept of set, for the theory of sets and for the philosophy and foundations of mathematics.

scholarly journals CAN MODALITIES SAVE NAIVE SET THEORY?

2017 ◽  
Vol 11 (1) ◽  
pp. 21-47
Author(s):  
PETER FRITZ ◽  
HARVEY LEDERMAN ◽  
TIANKAI LIU ◽  
DANA SCOTT
Keyword(s):  
Set Theory ◽  
Stanford University ◽  
Palo Alto ◽  
Naive Set Theory

To the memory of Prof. Grigori Mints, Stanford UniversityBorn: June 7, 1939, St. Petersburg, RussiaDied: May 29, 2014, Palo Alto, California

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