On Harrington's model in which Separation holds but Reduction fails at the 3rd projective level, and on some related models of Sami

Vassily Lyubetsky; Vladimir Kanovei

arxiv: 1810.12542 · v2 · pith:56TNFAZOnew · submitted 2018-10-30 · 🧮 math.LO

On Harrington's model in which Separation holds but Reduction fails at the 3rd projective level, and on some related models of Sami

Vladimir Kanovei , Vassily Lyubetsky This is my paper

classification 🧮 math.LO

keywords failsharringtonholdsmathbfmodelreductionseparationanything

0 comments

read the original abstract

In a handwtitten note of 1975, Leo Harrington sketched a construction of a model of ZFC (no large cardinals or anything beyond ZFC!) in which $\mathbf\Pi^1_3$-Separation holds but $\mathbf\Sigma^1_3$-Reduction fails. The result has never appeared in a journal or book publication except for a few of old references.

This paper has not been read by Pith yet.

On Harrington's model in which Separation holds but Reduction fails at the 3rd projective level, and on some related models of Sami

discussion (0)