11,469 research outputs found
Preserving levels of projective determinacy by tree forcings
We prove that various classical tree forcings -- for instance Sacks forcing,
Mathias forcing, Laver forcing, Miller forcing and Silver forcing -- preserve
the statement that every real has a sharp and hence analytic determinacy. We
then lift this result via methods of inner model theory to obtain
level-by-level preservation of projective determinacy (PD). Assuming PD, we
further prove that projective generic absoluteness holds and no new equivalence
classes classes are added to thin projective transitive relations by these
forcings.Comment: 3 figure
Techniques for approaching the dual Ramsey property in the projective hierarchy
We define the dualizations of objects and concepts which are essential for
investigating the Ramsey property in the first levels of the projective
hierarchy, prove a forcing equivalence theorem for dual Mathias forcing and
dual Laver forcing, and show that the Harrington-Kechris techniques for proving
the Ramsey property from determinacy work in the dualized case as well
Slow Forcing in the Projective Dynamics Method
We provide a proof that when there is no forcing the recently introduced
projective dynamics Monte Carlo algorithm gives the exact lifetime of the
metastable state, within statistical uncertainties. We also show numerical
evidence illustrating that for slow forcing the approach to the zero-forcing
limit is rather rapid. The model studied numerically is the 3-dimensional
3-state Potts ferromagnet.Comment: 1 figure, invited submission to CCP'98 conference, submitted to
Computer Physics Communication
Incompatible bounded category forcing axioms
We introduce bounded category forcing axioms for well-behaved classes
. These are strong forms of bounded forcing axioms which completely
decide the theory of some initial segment of the universe
modulo forcing in , for some cardinal
naturally associated to . These axioms naturally
extend projective absoluteness for arbitrary set-forcing--in this situation
--to classes with .
Unlike projective absoluteness, these higher bounded category forcing axioms do
not follow from large cardinal axioms, but can be forced under mild large
cardinal assumptions on . We also show the existence of many classes
with , and giving rise to pairwise
incompatible theories for .Comment: arXiv admin note: substantial text overlap with arXiv:1805.0873
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