Switch-reference has been analyzed as a reference tracking mechanism, whose main function is to avoid ambiguity of reference. One domain where this function has been argued to manifest itself is referential choice. Kibrik (Kibrik, Andrej. 2011. Reference in discourse. Oxford: Oxford University Press) notably proposed that switch-reference marking plays the role of a referential aid, which helps to prevent referential conflict, thereby enabling the production of reduced referential expressions such as pronouns and zeros. The present study probes this theory through an analysis of the role of switch-reference marking in multifactorial models of referential choice in Mbyá Guaraní. We show that while switch-reference increases the likelihood of mention reduction in Mbyá Guaraní, this effect is marginal relative to other predictors of referential choice. We argue that this result is compatible with the analysis of switch-reference as a referential aid, but also supports analyses that emphasize the multiplicity of its functions, beyond the disambiguation of reference.
It is known that if a subset of
R
\mathbb {R}
has positive Lebesgue measure, then it contains arbitrarily long finite arithmetic progressions. We prove that this result does not extend to infinite arithmetic progressions in the following sense: for each
λ
\lambda
in
[
0
,
1
)
[0,1)
, we construct a subset of
R
\mathbb {R}
that intersects every interval of unit length in a set of measure at least
λ
\lambda
, but that does not contain any infinite arithmetic progression.
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