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The practice of first-order logic is replete with meta-level concepts. Most notably there are the meta-variables themselves (ranging over predicates, variables, and terms), assumptions about freshness of variables with respect to these meta-variables, alpha-equivalence and capture-avoiding substitution. We present one-and-a-halfthorder logic, in which these concepts are made explicit. We exhibit both algebraic and sequent specifications of one-and-a-halfth-order logic derivability, show themdoi:10.1145/1140335.1140359 dblp:conf/ppdp/GabbayM06 fatcat:sbvrcyvv7bac5h5p2wjdmbdwia