Things that can be made into themselves

Things that can be made into themselves

One says that a property P of sets of natural numbers can be made into itself iff there is a numbering α0, α1, . . . of all left-r.e. sets such that the index set {e : αe satisfies P} has the property P as well. For example, the property of being Martin-Löf random can be made into itself. Herein we characterize those singleton properties which can be made into themselves. A second direction of ...

Things That Change by Themselves

Some fluents (for instance, time) change even after events that are not assumed to affect them (such as the action wait). We propose a formal-ization of the "commonsense law of inertia" in the situation calculus that allows us to describe such fluents. 1 Introduction The frame problem in Artificial Intelligence is the problem of specifying formally "what doesn't change when an event occurs" in ...

Things that can and things that can ’ t be done in PRA Ulrich

Things That Can and Things That Cannot Be Done in PRA

Things that can and things that can’t be done in PRA

It is well-known by now that large parts of (non-constructive) mathematical reasoning can be carried out in systems T which are conservative over primitive recursive arithmetic PRA (and even much weaker systems). On the other hand there are principles S of elementary analysis (like the Bolzano-Weierstraß principle, the existence of a limit superior for bounded sequences etc.) which are known to...