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://www.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},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {2014},
    Month = {Jan},
    URL = {http://www.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://www.eecs.berkeley.edu/Pubs/TechRpts/2014/EECS-2014-7.html
%F Matsikoudis:EECS-2014-7