The importance of the comparative notion of verisimilitude, or truthli
keness, for a realist conception of knowledge follows from two modest
'realist' assumptions, namely, that the aim of an enquiry, as an enqui
ry, is the truth of some matter; and that one false theory may realize
this aim better than another. However, there seem to be two ways in w
hich one (false) theory can realize this aim better than another. One
(false) theory can be closer to the truth than another either by being
preponderantly more accurate in its predictions or by providing more
comprehensive information about the system (or class of systems) at is
sue. This paper presents a model-theoretic approach to the analysis of
the comprehensiveness-related component of the comparative notion of
verisimilitude. The machinery of the 'semantic' view of theories is ap
plied to the problem of providing necessary and sufficient conditions
for the truth of sentences of the form, 'B is truth-increasing with re
spect to A', where A and B are taken to be sets of structures.