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.

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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