Timeline for What is a 'power admissible model'?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 23, 2016 at 10:47 | vote | accept | Stefan Mesken | ||
| Dec 23, 2016 at 10:46 | comment | added | Stefan Mesken | Right. On first instinct I thought that adding the predicate $\mathcal{P}$ may end up pushing the complexity of the powerset axiom to $\Delta_0^{\mathcal{P}}$, but that's not the case. After checking the papers once again, I'm fairly convinced that Steel's power admissibility is the one you linked to, but without the powerset axiom. Thanks for your help! | |
| Dec 22, 2016 at 18:40 | comment | added | Juan | Recall that you only have $\Delta_0^{\mathcal{P}}$-collection and separation! (Although Adrian shows that the $\Delta_1^{\mathcal{P}}$ versions follow) This does not let you do much with power sets, since the power-set axiom has a higher complexity. Thus, adding the power-set operator as primitive sidesteps this and results in a stronger theory. | |
| Dec 22, 2016 at 18:26 | comment | added | Stefan Mesken | In this paper, Mathias also includes the axiom of infinity and the powerset axiom in $\operatorname{KP}^{\mathcal{P}}$. Infinity is fine with me, as it will always hold in the structures I am interested in. Also, since all my models are transitive, I have full foundation for free. However, the powerset axiom typically fails. Including the powerset axiom in $\operatorname{KP}^{\mathcal{P}}$ seems curious to me, as - on first sight - it appears to render the additional predicate $\mathcal{P}$ rather pointless... I'll think about it for a little while. | |
| Dec 22, 2016 at 17:24 | history | answered | Juan | CC BY-SA 3.0 |