Timeline for Forcing in Second-Order Arithmetic
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Nov 28, 2016 at 5:43 | vote | accept | Thomas Benjamin | ||
| Nov 28, 2016 at 0:12 | comment | added | Andreas Blass | @HenryTowsner My guess as to what "sets of integers form a proper class" might mean is that the OP wants a model that is not a set (in the metatheory) but a proper class. Another way to think of that would be to start with an inaccessible cardinal $\kappa$ (again in the metatheory), force to adjoin $\kappa$ new reals (e.g., Cohen reals), and then retreat to a viewpoint where $V_\kappa$ is regarded as the whole set-theoretic universe. | |
| Nov 27, 2016 at 18:33 | answer | added | Noah Schweber | timeline score: 6 | |
| Nov 27, 2016 at 17:56 | comment | added | Henry Towsner | 2) Constructions that are essentially forcing already appears in Simpson's book, and a search for "forcing reverse mathematics" turns up many references, both to recursion-theoretic forcing (which may not be quite what you're asking for, since the sets are constructible) and to Steel forcing (which does use nonconstructible sets). It might help to explain whether, in particular, Steel forcing is or isn't the sort of thing you're asking about. | |
| Nov 27, 2016 at 17:51 | comment | added | Henry Towsner | I'm having some trouble understanding this question. 1) what does it mean for "sets of integers to form a proper class"? In SOA there is no notion of "proper class", and in ZFC, the subsets of some fixed set (the universe of the model) can't be a proper class, so there can be no model of SOA whose collection of sets are not bijective with a set. | |
| S Nov 27, 2016 at 17:15 | history | suggested | Martin Sleziak |
added top-level tag; http://meta.mathoverflow.net/questions/1457/why-are-mo-tags-formatted-as-they-are
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| Nov 27, 2016 at 17:03 | review | Suggested edits | |||
| S Nov 27, 2016 at 17:15 | |||||
| Nov 27, 2016 at 16:54 | history | asked | Thomas Benjamin | CC BY-SA 3.0 |