A method for proving something about all sets in ZFC

[phoenixthoth]

I would appreciate any and all feedback regarding this document currently housed in Google docs. Basically, I generalize induction among natural numbers to an extreme in an environment regarding what I call grammatical systems. Then an induction principle is derived from that which holds in ZFC set theory (and perhaps other set theories) which would enable someone to prove statements about all sets in ZFC.

https://docs.google.com/document/d/1amDb4Yti4egpKfcO2oLcnGAH8UpC8_tKb7ivuH3AT7A/edit?usp=sharing

 

[micromass]

So what kind of feedback do you want? Everything in the document is rather well-known, it's only phrased in terms that are pretty weird. There are some inaccurate things in the document though, so perhaps you want to discuss that?

 

[micromass]

In particular, take a look at section 1.2 of Hinman's "Fundamentals of logic". You should be more careful in your document however since you only define "grammatical systems" for sets, while you later use them for classes when dealing with ZF.

 

[phoenixthoth]

So what kind of feedback do you want? Everything in the document is rather well-known, it's only phrased in terms that are pretty weird. There are some inaccurate things in the document though, so perhaps you want to discuss that?

That in itself is very useful feedback. Thank you. I guess I haven't studied enough set theory because I haven't seen this result before. I'm glad I don't have to reinvent the wheel. I will see if I can find Hinman. We might as well discuss those innacurate things. I don't know if changing the terms I use from sets to classes when defining grammatical systems would harm anything. I was also thinking, alternatively, that maybe I should note that I must not be working within ZFC in order to prove something about ZFC; I apparently need something else like NFU or something that isn't ZFC. I'm excited to go find out other presentations of this result which I was suspecting was well-known, in part to see if more or less machinery is required in other presentations.

 

[phoenixthoth]

Are there any references online that explain this result differently from how I did it (or almost did it) as I cannot find Hinman's book online?