Timeline for $Δ^1_3$ reals in transitive models
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 9 at 3:00 | comment | added | Dmytro Taranovsky | Correction: For the $Δ^1_1$ definability in $ω$-models sentence, "$0^{\text{HJ}}$ does not exist" does not seem right/sufficient. A possible correction: One can ask whether for every real $x$ such that no hyperarithmetic-in-$x$ real encodes an iteration of arithmetic comprehension (starting at 0) along an ill-founded order, $x$ is $Δ^1_1$ definable in some $ω$-model of ZFC\P. | |
| Oct 8 at 23:57 | comment | added | Farmer S | Right, I started to figure so. Will delete the answer... | |
| Oct 8 at 23:57 | comment | added | Dmytro Taranovsky | Correct. It means your (ii). | |
| Oct 8 at 23:53 | comment | added | Farmer S | Hmm, I just wrote an answer, but I now realise I may have misunderstood your terminology. By "x is Delta^1_3 in M" do you mean (i) "x is Delta^1_3({M})", i.e. Delta^1_3-definable from the parameter M (meaning uniformly in reals coding M), or do you mean (ii) "x is in M and M models `x is Delta^1_3-definable'"? I was reading it as (i), hence the answer, but I presume now it is (ii), is that right? | |
| Oct 8 at 19:32 | history | asked | Dmytro Taranovsky | CC BY-SA 4.0 |