scholarly journals The Axiom of Choice: The Last Great Controversy in Mathematics

2021 ◽  
Author(s):  
Josephine Hulkewicz
Keyword(s):  
Axiom Of Choice ◽  
Multiple Perspectives ◽  
The Axiom Of Choice ◽  
Potential Use

This paper explores multiple perspectives and proofs regarding the validity of what is considered to be one of the – if not THE - most controversial proofs in the field of mathematics, historical and contemporary applications alike. We consider the various explanations and equivalents of the axiom along with the more widely receptive alternatives. Furthermore, we review the resistance the axiom has encountered in various fields and its potential use in the research and expansion of said fields.

The Axiom of Choice Machine

2018 ◽  
Author(s):  
Alexander R. Pruss
Keyword(s):  
Set Theory ◽  
Laws Of Nature ◽  
Axiom Of Choice ◽  
Dutch Book ◽  
The Axiom Of Choice

This is a mainly technical chapter concerning the causal embodiment of the Axiom of Choice from set theory. The Axiom of Choice powered a construction of an infinite fair lottery in Chapter 4 and a die-rolling strategy in Chapter 5. For those applications to work, there has to be a causally implementable (though perhaps not compatible with our laws of nature) way to implement the Axiom of Choice—and, for our purposes, it is ideal if that involves infinite causal histories, so the causal finitist can reject it. Such a construction is offered. Moreover, other paradoxes involving the Axiom of Choice are given, including two Dutch Book paradoxes connected with the Banach–Tarski paradox. Again, all this is argued to provide evidence for causal finitism.

scholarly journals The relationship between two weak forms of the axiom of choice

1973 ◽  
Vol 80 (1) ◽  
pp. 75-79 ◽  
Author(s):  
Paul Howard ◽  
Herman Rubin ◽  
Jean Rubin
Keyword(s):  
Axiom Of Choice ◽  
The Axiom Of Choice ◽  
The Relationship
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