We introduce FMG (Fraenkel-Mostowski Generalised) set theory, a generalisation of FM set theory which allows binding of infinitely many names instead of just finitely many names. We apply this generalisation to show how three presentations of syntax-de Bruijn indices, FM sets, and name-carrying syntax-have a relation generalising to all sets and not only sets of syntax trees. We also give syntax-free accounts of Barendregt representatives, scope extrusion, and other phenomena associated to α-equivalence. Our presentation uses a novel presentation based not on a theory but on a concrete model U. © 2007 Elsevier Inc. All rights reserved.
CITATION STYLE
Gabbay, M. J. (2007). A general mathematics of names. Information and Computation, 205(7), 982–1011. https://doi.org/10.1016/j.ic.2006.10.010
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