A general mathematics of names

  • Gabbay M
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Abstract

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.

Author-supplied keywords

  • Alpha-conversion
  • Fraenkel-Mostowski set theory
  • NEW quantifier
  • Names
  • Nominal techniques
  • Set theory

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Authors

  • Murdoch J. Gabbay

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