Example[]
What set is \(L_1\)?C7X (talk) 13:34, February 10, 2020 (UTC)
- I added the answer to the article.
- p-adic 13:56, February 10, 2020 (UTC)
Indiscernibility[]
Is this correct?
"For example (assuming existence of \(0^\sharp\)), there are indiscernible members of \(\mathcal P(\omega)\) that are members of \(V_{\omega+1}\), but not \(L_{\omega+1}\)." C7X (talk) 15:05, 22 November 2020 (UTC)
- I am not sure, because I do not know a precise definition of the indiscernibility. If you have a source of the statement, it is good to write the information togerther with the source. If you do not have a source of the statement but you have a source of the definition and a proof, then it is good to write the definition together with the source and a proof. (And I guess that you do not have a proof, since you are asking here.)
- p-adic 00:57, 23 November 2020 (UTC)
- This is a statement that I wrote myself, and if it's correct I think it can be helpful to include. This is a possible way to formulate indiscernibility:
- A set \(s\) is indiscernible iff there is no {∈}-formula \(\phi(x)\) with exactly one free variable such that \(\forall y(\phi(y)\leftrightarrow y=s)\)
- If it is a standard convention, we should follow the traditional definition. If the tranditinal definition quantifies φ, then it is better to cite the definition and follow the definition. (Also, you are not using parameters from L_ω, right?) I am not certain about the correctness. Is there a theorem under 0# that P(ω) ⊂ L? How do we deduce the argument on V without relativising φ's to L?
- p-adic 02:41, 23 November 2020 (UTC)