Notions of indifference for genericity: Union and subsequence sets

04/28/2021
by   Tejas Bhojraj, et al.
0

A set I is said to be a universal indifferent set for 1-genericity if for every 1-generic G and for all X ⊆ I, G Δ X is also 1-generic. Miller showed that there is no infinite universal indifferent set for 1-genericity. We introduce two variants (union and subsequence sets for 1-genericity) of the notion of universal indifference and prove that there are no non-trivial universal sets for 1-genericity with respect to these notions. In contrast, we show that there is a non-computable subsequence set for weak-1-genericity.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
01/25/2013

Approximation of Classification and Measures of Uncertainty in Rough Set on Two Universal Sets

The notion of rough set captures indiscernibility of elements in a set. ...
research
06/15/2021

Rice's theorem for generic limit sets of cellular automata

The generic limit set of a cellular automaton is a topologically dened s...
research
06/22/2018

A Universal Hypercomputer

This paper describes a type of infinitary computer (a hypercomputer) cap...
research
06/30/2023

A Framework for Universality in Physics, Computer Science, and Beyond

Turing machines and spin models share a notion of universality according...
research
01/16/2020

Lower density selection schemes via small universal hitting sets with short remaining path length

Universal hitting sets are sets of words that are unavoidable: every lon...
research
04/27/2023

Universal Obstructions of Graph Parameters

We introduce a graph-parametric framework for obtaining obstruction char...
research
09/11/2007

On Universal Prediction and Bayesian Confirmation

The Bayesian framework is a well-studied and successful framework for in...

Please sign up or login with your details

Forgot password? Click here to reset