# 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