FORCING WITH BUSHY TREES.

We present several results that rely on arguments involving the combinatorics of "bushy trees". These include the fact that there are arbitrarily slow-growing diagonally noncomputable(DNC) functions that compute noKurtz random real, as well as an extension of a result of Kumabe in which we establish...

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Detalles Bibliográficos
Publicado en:	Bulletin of Symbolic Logic Vol. 23; no. 2; pp. 160 - 181
Autores principales:	KHAN, MUSHFEQ, MILLER, JOSEPH S.
Formato:	Artículo
Publicado:	Cambridge University Press Jun2017
Materias:	Asparagus densiflorus Forcing (Model theory) Algorithmic randomness Computable model theory Turing (Computer program language)
Acceso en línea:	Ver este registro en EBSCOhost

Descripción
Sumario:	We present several results that rely on arguments involving the combinatorics of "bushy trees". These include the fact that there are arbitrarily slow-growing diagonally noncomputable(DNC) functions that compute noKurtz random real, as well as an extension of a result of Kumabe in which we establish that there are DNC functions relative to arbitrary oracles that are of minimal Turing degree. Along the way, we survey some of the existing instances of bushy tree arguments in the literature.