A general mathematics of names

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 syntaxfree 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. Key words: Set theory, Fraenkel-Mostowski set theory, NEW quantifier, nominal techniques, alpha-conversion, names. Contents

• Type: Journal
• Year: 2007
• Where: IANDC
• Authors: Murdoch Gabbay
• Keywords: Generalisation, IANDC 2007, Presentation, Theory