We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
EQUIVALENCE RELATIONS WHICH ARE BOREL SOMEWHERE.
- Authors
CHAN, WILLIAM
- Abstract
The following will be shown: Let I be a σ-ideal on a Polish space X so that the associated forcing of I+${\bf{\Delta }}_1^1$ sets ordered by ⊆ is a proper forcing. Let E be a ${\bf{\Sigma }}_1^1$ or a ${\bf{\Pi }}_1^1$ equivalence relation on X with all equivalence classes ${\bf{\Delta }}_1^1$. If for all $z \in {H_{{{\left( {{2^{{\aleph _0}}}} \right)}^ + }}}$, z♯ exists, then there exists an I+${\bf{\Delta }}_1^1$ set C ⊆ X such that E ↾ C is a ${\bf{\Delta }}_1^1$ equivalence relation.
- Subjects
BOREL sets; MATHEMATICAL equivalence; MATHEMATICAL continuum; SET theory; LEBESGUE measure; DEFINABILITY theory (Mathematical logic)
- Publication
Journal of Symbolic Logic, 2017, Vol 82, Issue 3, p893
- ISSN
0022-4812
- Publication type
Article
- DOI
10.1017/jsl.2017.22