Generalized Ultrametric Semilattices of Linear Signals
Eleftherios Matsikoudis and Edward A. Lee
EECS Department, University of California, Berkeley
Technical Report No. UCB/EECS-2014-7
January 23, 2014
http://www2.eecs.berkeley.edu/Pubs/TechRpts/2014/EECS-2014-7.pdf
We consider certain spaces of linear signals equipped with a standard prefix relation and a suitably defined generalized distance function. We introduce a new class of abstract structures, which we call generalized ultrametric semilattices, and prove a representation theorem stating that every generalized ultrametric semilattice with a totally ordered distance set is isomorphic to a space of that kind. It follows that the formal definition of generalized ultrametric semilattices with totally ordered distance sets constitutes an axiomatization of the first-order theory of those spaces.
BibTeX citation:
@techreport{Matsikoudis:EECS-2014-7, Author= {Matsikoudis, Eleftherios and Lee, Edward A.}, Title= {Generalized Ultrametric Semilattices of Linear Signals}, Year= {2014}, Month= {Jan}, Url= {http://www2.eecs.berkeley.edu/Pubs/TechRpts/2014/EECS-2014-7.html}, Number= {UCB/EECS-2014-7}, Abstract= {We consider certain spaces of linear signals equipped with a standard prefix relation and a suitably defined generalized distance function. We introduce a new class of abstract structures, which we call generalized ultrametric semilattices, and prove a representation theorem stating that every generalized ultrametric semilattice with a totally ordered distance set is isomorphic to a space of that kind. It follows that the formal definition of generalized ultrametric semilattices with totally ordered distance sets constitutes an axiomatization of the first-order theory of those spaces.}, }
EndNote citation:
%0 Report %A Matsikoudis, Eleftherios %A Lee, Edward A. %T Generalized Ultrametric Semilattices of Linear Signals %I EECS Department, University of California, Berkeley %D 2014 %8 January 23 %@ UCB/EECS-2014-7 %U http://www2.eecs.berkeley.edu/Pubs/TechRpts/2014/EECS-2014-7.html %F Matsikoudis:EECS-2014-7