860 research outputs found
Oral History Interview with Tony Tan Keng Yam: Conceptualising SMU
This is an abridged version of the original interview. Please contact the Library at [email protected] for access to the full version of the transcript and/or audio recording.</p
A note on first-order spectra with binary relations
The spectrum of a first-order sentence is the set of the cardinalities of its
finite models. In this paper, we consider the spectra of sentences over binary
relations that use at least three variables. We show that for every such
sentence , there is a sentence that uses the same number of
variables, but only one symmetric binary relation, such that its spectrum is
linearly proportional to the spectrum of . Moreover, the models of
are all bipartite graphs. As a corollary, we obtain that to settle
Asser's conjecture, i.e., whether the class of spectra is closed under
complement, it is sufficient to consider only sentences using only three
variables whose models are restricted to undirected bipartite graphs
Approximating polygonal objects with deformable smooth surfaces
Master'sMASTER OF SCIENC
- …