Timeline for Absoluteness and Tree Representations
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Apr 15, 2016 at 6:20 | vote | accept | William | ||
| Feb 9, 2016 at 22:47 | comment | added | Rachid Atmai | @William Exactly, that's the idea. The more sets you can show are $Hom_{\infty}$, the more formulae you can express in a $(\Sigma^2_1)^{Hom_{\infty}}$ way and this buys you more absoluteness. $\psi$ is $(\Sigma^2_1)^{Hom_{\infty}}$ if it is of the form $\exists A\in Hom_{\infty} (HC,\in,A)\models \varphi$, some $\varphi$. $(HC,\in,A)\models \varphi$ is projective. This is theorem 5.1 in Steel's paper. 5.6 explains the reduction of $L(\mathbb{R})$-truth to $(\Sigma^2_1)^{Hom_{\infty}}$-truth. The part about the tree production is not really relevant, it just offers uB representation. | |
| Feb 9, 2016 at 18:42 | comment | added | William | Thanks very much for your reference. Just one question: I could not find explicitly the definition of $(\Sigma_2^1)^{\text{Hom}_{<\lambda}}$ in Steel's paper, but I get the impression that they are formulas of the kind that appear in Theorem 5.1 of Steel's paper. For my question, if $A$ is homogeneously Suslin, both $A$ and $(\forall y)A$ are $(\Sigma_2^1)^{\text{Hom}_{<\lambda}}$ formulas and so Theorem 5.1 would give the desired absoluteness. Is this the idea? Thanks | |
| Feb 8, 2016 at 13:13 | history | answered | Rachid Atmai | CC BY-SA 3.0 |