# Table of Contents

-   [`[2017-11-30]` Continuum hypothesis](#cntnmhypthss) 
-   [`[2015-08-26]` depenedent sum](#dpndntsm) 
-   [Self-reference elimination: use indices](#slfrfrnclmntnsndcs) 





# `[2017-11-30]` Continuum hypothesis

Godel: proved that ZFC + CH is consistnent  
Cohen: proved that ZFC + ~CH is consistnent (actually, any intermediate number of infinities)  




# `[2015-08-26]` depenedent sum

Sum    (a : A) (B(A)) = {(a, b) | a ∈ A, b ∈ B(a)}  
Exists (a : A) (B(A)) = || Sum a B ||  




# Self-reference elimination: use indices

x<sup>1</sup> &isin; y<sup>2</sup>  

y<sup>2</sup> &isin; x<sup>1</sup>: forbidden!  
x<sup>1</sup> &isin; x<sup>2</sup>: forbidden!  

System NF?