Logic

Table of Contents

• [2017-11-30] Continuum hypothesis
• [2015-08-26] depenedent sum
• [[Self-reference elimination: use indices]]

[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

x¹ ∈ y²

y² ∈ x¹: forbidden!
x¹ ∈ x²: forbidden!

System NF?

• [[yog]] https://mathstodon.xyz/@yog/109251697238446888 pull
• [[yog]] https://mathstodon.xyz/@yog/109251675571431146 pull