Abstract



What are variables, and what is universal quanti?cation over a variable? Nominal sets are a notion of ?sets with names?, and using equational axioms in nominal algebra these names can be given substitution and quanti?cation actions. So we can axiomatise ?rstorder logic as a nominal logical theory. We can then seek a nominal sets representation theorem in which predicates are interpreted as sets; logical conjunction is interpreted as sets intersection; negation as complement. Now what about substitution; what is it for substitution to act on a predicateinterpretedasaset, in which case universal quanti?cation becomes an in?nite sets intersection? Given answers to these questions, we can seek notions of topology. What is the general notion of topological space of which our sets representation of predicates makes predicates into ?open sets?; and what speci?c class of topological spaces corresponds to the image of nominal algebras for ?rstorder logic? The classic Stone duality answers these questions for Boolean algebras, representing them as Stone spaces. Nominal algebra lets us extend Boolean algebras to ?FOLalgebras?, and nominal sets let us correspondingly extend Stone spaces to ?8Stone spaces?. These extensions reveal a wealth of structure, and we obtain an attractive and selfcontained account of logic and topology in which variables directly populate the denotation, and open predicates are interpreted as sets rather than functions from valuations to sets. Keywords: Stone duality, nominal sets, ?rstorder logic, topology, variables  
International

Si 


Book Edition


Book Publishing


ISBN

9783642229435 
Series


Book title

Festschrifft in honour of Edward Barringer 
From page

20 
To page

49 