Three Variables Suffice for Real-Time Logic
نویسندگان
چکیده
A natural framework for real-time specification is monadic first-order logic over the structure (R, <,+1)—the ordered real line with unary +1 function. Our main result is that (R, <,+1) has the 3-variable property: every monadic first-order formula with at most 3 free variables is equivalent over this structure to one that uses 3 variables in total. As a corollary we obtain also the 3-variable property for the structure (R, <, f) for any fixed linear function f : R→ R. On the other hand we exhibit a countable dense linear order (E,<) and a bijection f : E → E such that (E,<, f) does not have the k-variable property for any k.
منابع مشابه
Three Variables Suffice for Real-Time Specification
A natural framework for real-time specification is monadic first-order logic over the structure (R, <,+1)—the ordered real line with unary +1 function. Our main result is that (R, <,+1) has the 3-variable property: every monadic first-order formula with at most 3 free variables is equivalent over this structure to one that uses 3 variables in total. As a corollary we obtain also the 3-variable ...
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