MoL199904: Dean, Walter (1999) Three Recursion Theoretic Concepts of Genericity. [Report]
Text (Full Text)
MoL199904.text.ps.gz Download (110kB) 

Text (Abstract)
MoL199904.abstract.txt Download (1kB) 
Abstract
This paper develops and contrasts three recursiontheoretic notions of
genericity: one for sets below 0', and two for the recursively enumerable
(r.e.) sets. The first is the classical notion of 1genericity, developed
in the context of the finite extension method first developed by Kleene
and Post to study degrees below 0'. We review several established
facts about 1generic sets showing that they are biimmune, generalized
low and have Turing incomparable even and odd halves. We then generalize
the definition of 1genericity to obtain a noneffective version of a
result of Sacks which states that for any r.e. nonrecursive C there is
a simple set A such that C <=_T A. We next develop a new notion of
genericity based on the EllentuckMathias [EM] topology on 2^\omega.
EMgeneric sets are shown to be simple and have Turing incomparable
even and odd halves. Finally we introduce and generalize a concept of
Jockusch known as egenericity and show how it can be modified so as to
obtain the full results of Sacks stated above.
Item Type:  Report 

Report Nr:  MoL199904 
Series Name:  Master of Logic Thesis (MoL) Series 
Year:  1999 
Date Deposited:  12 Oct 2016 14:38 
Last Modified:  12 Oct 2016 14:38 
URI:  https://eprints.illc.uva.nl/id/eprint/707 
Actions (login required)
View Item 