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- Title
An unpublished theorem of Solovay on OD partitions of reals into two non-OD parts, revisited.
- Authors
Enayat, Ali; Kanovei, Vladimir
- Abstract
A definable pair of disjoint non-OD sets of reals (hence, indiscernible sets) exists in the Sacks and 0-large generic extensions of the constructible universe L. More specifically, if a ∈ 2 ω is either Sacks generic or 0-large generic real over L, then it is true in L[a] that there is a lightface Π 2 1 equivalence relation Q on the Π 2 1 set U = 2 ω \ L with exactly two equivalence classes, and both those classes are non-OD sets.
- Subjects
EQUIVALENCE relations (Set theory); PARTITIONS (Mathematics)
- Publication
Journal of Mathematical Logic, 2021, Vol 21, Issue 3, p1
- ISSN
0219-0613
- Publication type
Article
- DOI
10.1142/S0219061321500148