A general mathematics of names

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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
Murdoch Gabbay
Added 14 Dec 2010
Updated 14 Dec 2010
Type Journal
Year 2007
Authors Murdoch Gabbay
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