Matches in SemOpenAlex for { <https://semopenalex.org/work/W2158946156> ?p ?o ?g. }
Showing items 1 to 76 of
76
with 100 items per page.
- W2158946156 endingPage "184" @default.
- W2158946156 startingPage "176" @default.
- W2158946156 abstract "The present paper investigates the power of proper forcings to change the shape of the universe, in a certain well-defined respect. It turns out that the ranking among large cardinals can be used as a measure for that power. However, in order to establish the final result I had to isolate a new large cardinal concept, which I dubbed “remarkability.” Let us approach the exact formulation of the problem—and of its solution—at a slow pace. Breathtaking developments in the mid 1980s found one of its culminations in the theorem, due to Martin, Steel, and Woodin, that the existence of infinitely many Woodin cardinals with a measurable cardinal above them all implies that AD, the axiom of determinacy, holds in the least inner model containing all the reals, L(ℝ) (cf. [6[, p. 91). One of the nice things about AD is that the theory ZF + AD + V = L (ℝ) appears as a choiceless “completion” of ZF in that any interesting question (in particular, about sets of reals) seems to find an at least attractive answer in that theory (cf., for example, [5] Chap. 6). (Compare with ZF + V = L!) Beyond that, AD is very canonical as may be illustrated as follows. Let us say that L(ℝ) is absolute for set-sized forcings if for all posets P ∈ V, for all formulae ϕ, and for all ∈ ℝ do we have that where is a name for the set of reals in the extension." @default.
- W2158946156 created "2016-06-24" @default.
- W2158946156 creator A5025902803 @default.
- W2158946156 date "2000-06-01" @default.
- W2158946156 modified "2023-09-24" @default.
- W2158946156 title "Proper Forcing and Remarkable Cardinals" @default.
- W2158946156 cites W1505039805 @default.
- W2158946156 cites W1594209351 @default.
- W2158946156 cites W2007638330 @default.
- W2158946156 cites W2049652789 @default.
- W2158946156 cites W2051090768 @default.
- W2158946156 cites W2117873821 @default.
- W2158946156 cites W4248490242 @default.
- W2158946156 doi "https://doi.org/10.2307/421205" @default.
- W2158946156 hasPublicationYear "2000" @default.
- W2158946156 type Work @default.
- W2158946156 sameAs 2158946156 @default.
- W2158946156 citedByCount "34" @default.
- W2158946156 countsByYear W21589461562013 @default.
- W2158946156 countsByYear W21589461562014 @default.
- W2158946156 countsByYear W21589461562015 @default.
- W2158946156 countsByYear W21589461562016 @default.
- W2158946156 countsByYear W21589461562017 @default.
- W2158946156 countsByYear W21589461562018 @default.
- W2158946156 countsByYear W21589461562019 @default.
- W2158946156 countsByYear W21589461562021 @default.
- W2158946156 countsByYear W21589461562023 @default.
- W2158946156 crossrefType "journal-article" @default.
- W2158946156 hasAuthorship W2158946156A5025902803 @default.
- W2158946156 hasConcept C114614502 @default.
- W2158946156 hasConcept C118615104 @default.
- W2158946156 hasConcept C134306372 @default.
- W2158946156 hasConcept C151797676 @default.
- W2158946156 hasConcept C153046414 @default.
- W2158946156 hasConcept C167729594 @default.
- W2158946156 hasConcept C177264268 @default.
- W2158946156 hasConcept C197115733 @default.
- W2158946156 hasConcept C199360897 @default.
- W2158946156 hasConcept C2524010 @default.
- W2158946156 hasConcept C2778029271 @default.
- W2158946156 hasConcept C33923547 @default.
- W2158946156 hasConcept C41008148 @default.
- W2158946156 hasConceptScore W2158946156C114614502 @default.
- W2158946156 hasConceptScore W2158946156C118615104 @default.
- W2158946156 hasConceptScore W2158946156C134306372 @default.
- W2158946156 hasConceptScore W2158946156C151797676 @default.
- W2158946156 hasConceptScore W2158946156C153046414 @default.
- W2158946156 hasConceptScore W2158946156C167729594 @default.
- W2158946156 hasConceptScore W2158946156C177264268 @default.
- W2158946156 hasConceptScore W2158946156C197115733 @default.
- W2158946156 hasConceptScore W2158946156C199360897 @default.
- W2158946156 hasConceptScore W2158946156C2524010 @default.
- W2158946156 hasConceptScore W2158946156C2778029271 @default.
- W2158946156 hasConceptScore W2158946156C33923547 @default.
- W2158946156 hasConceptScore W2158946156C41008148 @default.
- W2158946156 hasIssue "2" @default.
- W2158946156 hasLocation W21589461561 @default.
- W2158946156 hasOpenAccess W2158946156 @default.
- W2158946156 hasPrimaryLocation W21589461561 @default.
- W2158946156 hasRelatedWork W1981694349 @default.
- W2158946156 hasRelatedWork W2117235496 @default.
- W2158946156 hasRelatedWork W2250894200 @default.
- W2158946156 hasRelatedWork W2463235899 @default.
- W2158946156 hasRelatedWork W2467005568 @default.
- W2158946156 hasRelatedWork W2612116879 @default.
- W2158946156 hasRelatedWork W2950176801 @default.
- W2158946156 hasRelatedWork W2990062759 @default.
- W2158946156 hasRelatedWork W4230409512 @default.
- W2158946156 hasRelatedWork W4297781329 @default.
- W2158946156 hasVolume "6" @default.
- W2158946156 isParatext "false" @default.
- W2158946156 isRetracted "false" @default.
- W2158946156 magId "2158946156" @default.
- W2158946156 workType "article" @default.