(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

"Given a function H, assigning a value, 0 or 1, to each atomic sentence, define a sequence ℑ_{0}, ℑ_{1}, ℑ_{2}, ℑ_{3},... of functions, as follows:

ℑ_{0}is just H.

Given a function ℑn, assigning a value, either 0 or 1, to the sentences of degree less than or equal to n, define the function ℑn+1, assigning a value, either 0 or 1, to the sentences of degree less than or equal to n+1, as follows: If φ has degree less than or equal to n, ℑn+1(φ) = ℑn(φ)."

I confused with the english, (sorry i'm not good in english). please clarify this

H({0,1}) = ℑ_{0}, ℑ_{1}, ℑ_{2}, ℑ_{3},...

(does this mean "Given a function H, assigning a value, 0 or 1, to each atomic sentence, define a sequence ℑ"???)_{0}, ℑ_{1}, ℑ_{2}, ℑ_{3},... of functions

and what "as follows: ℑ" means? as follows? does is mean "such as"?_{0}is just H.

and i'll post the next question after this answered, because i wan to clear this first.

i'm sorry but the concise language is too concise for me i guess. help

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# Homework Help: Extension theorem (Existence)

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