A REAL OF STRICTLY POSITIVE EFFECTIVE PACKING DIMENSION THAT DOES NOT COMPUTE A REAL OF EFFECTIVE PACKING ONE.

Recently, the Dimension Problem for effective Hausdorff dimension was solved by J. Miller in [14], where the author constructs a Turing degree of non-integral Hausdorff-dimension. In this article we settle the Dimension Problem for effective packing dimension by constructing a real of strictly posit...

Descripción completa

Detalles Bibliográficos
Publicado en:	Journal of Symbolic Logic Vol. 77; no. 2; pp. 447 - 475
Autor principal:	Conidis, Chris J.
Formato:	Artículo
Publicado:	Cambridge University Press Jun2012
Materias:	Measure theory Hausdorff measures Algebraic topology Ring theory Fractals
Acceso en línea:	Ver este registro en EBSCOhost

Descripción
Sumario:	Recently, the Dimension Problem for effective Hausdorff dimension was solved by J. Miller in [14], where the author constructs a Turing degree of non-integral Hausdorff-dimension. In this article we settle the Dimension Problem for effective packing dimension by constructing a real of strictly positive effective packing dimension that does not compute a real of effective packing dimension one (on the other hand, it is known via [10, 3, 7] that every real of strictly positive effective Hausdorff dimension computes reals whose effective packing dimensions are arbitrarily close to, but not necessarily equal to, one).