Nominal sets are a sets-based first-order denotation for variables in logic and programming. In this paper we extend nominal sets to two-level nominal sets. These preserve much of the behaviour of nominal sets—including notions of variable and abstraction—but they include a denotation for variables and meta-variables. Meta-variables are interpreted as infinite lists of distinct variable symbols...

Nominal logic is an extension of first-order logic with features useful for reasoning about abstract syntax with bound names. For computational applications such as programming and formal reasoning, it is desirable to develop constructive type theories for nominal logic which extend standard type theories for propositional, firstor higher-order logic. This has proven difficult, largely because ...