March 11th, 2019, 05:47 PM  #11  
Senior Member Joined: Oct 2009 Posts: 752 Thanks: 261  Quote:
 
March 11th, 2019, 06:53 PM  #12 
Senior Member Joined: Jun 2014 From: USA Posts: 493 Thanks: 36  Yup. I don't adhere to restricted comprehension (such as the axiom schema of specification, etc.) in defining $A$, but since $A$ is enumerable I don't see the point of doing so. It matters not that I chose to apply a function to elements of the Alphabet as opposed to sets within the model. My definition is precise. Give me any set and we are able to tell precisely whether or not it is an element of $A$. The difference between $L_{\omega}$ and $A$ as I understand it would be any infinite elements of $L_{\omega}$. That's it. 
March 11th, 2019, 08:07 PM  #13 
Senior Member Joined: Aug 2012 Posts: 2,204 Thanks: 647  
March 11th, 2019, 08:30 PM  #14 
Senior Member Joined: Jun 2014 From: USA Posts: 493 Thanks: 36  Not if you still don't get what $A$ is. At this point, that would be you. I'm not sure you know what $L_{\omega}$ is either at this point, though I'm asking because I myself would like clarification. I've noted that $L_{\omega} = V_{\omega}$ and I want to make sure I understand why.

March 11th, 2019, 08:52 PM  #15  
Senior Member Joined: Aug 2012 Posts: 2,204 Thanks: 647  Quote:
 
March 12th, 2019, 05:02 AM  #16 
Senior Member Joined: Jun 2014 From: USA Posts: 493 Thanks: 36  
March 12th, 2019, 08:09 AM  #17 
Senior Member Joined: Jun 2014 From: USA Posts: 493 Thanks: 36 
A listing of the finite binary strings, $F$, could be used to construct $A$. $f^{1}[0] = \{$. This is not a set, so not in $A$. $f^{1}[1] = \}$. This is not a set, so not in $A$. $f^{1}[01] = \{\}$. This is a set, so in $A$. . . . $A = \{ x \in F : f^{1}[x] \text{ is a set} \}$. So what sets are in $L_{\omega}$ that are not in $A$? 
March 12th, 2019, 10:07 AM  #18 
Senior Member Joined: Aug 2012 Posts: 2,204 Thanks: 647  It would be immensely helpful to me if you would go over each of my posts in this thread, and each time you see a sentence ending in '?', please give a clear, straightforward response in simple, declarative sentences. Don't add anything and don't assume anything. Just answer each question.

March 13th, 2019, 08:57 AM  #19  
Senior Member Joined: Jun 2014 From: USA Posts: 493 Thanks: 36  Quote:
 
March 14th, 2019, 09:55 AM  #20 
Senior Member Joined: Aug 2012 Posts: 2,204 Thanks: 647  

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