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Fraenkel-Mostowksi set theory gives a model of substitution as
well as names

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Murdoch Gabbay, Heriot-Watt University

In my thesis I and Andrew Pitts gave a semantic model of
alpha-equivalence based on set theory. I will show, using only
elementary constructions, how this model extends to a semantic model
of *substitution*. This turns the set-theoretic universe into a
powerful generalisation of syntax, which raises intriguing
possibilities for denotations of rewriting and logic.
Further details can be found on my webpage
www.gabbay.org.uk