Cardinals (without the Axiom of Choice)

2017 ◽  
pp. 127-162
Keyword(s):  
Axiom Of Choice ◽  
The Axiom Of Choice

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
Sign in / Sign up

Export Citation Format

Share Document