abstract
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Magic sets

Lorenz Halbeisen, Marc Lischka, Salome Schumacher

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In this paper we study magic sets for certain families H
of real-valued functions,
which are subsets M of real numbers such
that for all functions f,g in H we have that g[M]
is a subset of f[M] if and only if f=g.
Specifically we are interested in magic sets for the
family G of all continuous functions that are not constant on any
open subset of R. We will show that these magic sets are stable
in the following sense: Adding and removing a countable set does
not destroy the property of being a magic set. Moreover, if
the union of less than c meager sets is still meager
(where c denotes the cardinality of the continuum),
we can also add and remove sets of cardinality
less than c without destroying the magic set.