Nominal techniques

The phrase nominal techniques is used to refer to various methods for modelling local and bound variables that depend on the view of names as atoms (in the sense of indivisibile ur-elements of some set theories).

The use of these techniques in Computer Science arose approx. after the year 2000.

Nominal techniques can be applied in both a set-theoretic and a category-theoretic setting.

Set-theoretically, nominal techniques can be developed over the Fraenkel-Mostowski universe, which is a model of ZFA. This language is used in the survey Gabbay 2011.
Category-theoretically, nominal sets are equivalent to the Schanuel topos.

References

A nice introductory survey to nominal techniques is given in

Pitts, Andrew. 2016. ‘Nominal Techniques’. ACM SIGLOG News 3 (1): 57–72. https://doi.org/10.1145/2893582.2893594.

@article{pitts_2016,
	title = {Nominal techniques},
	volume = {3},
	doi = {10.1145/2893582.2893594},
	number = {1},
	journal = {ACM SIGLOG News},
	author = {Pitts, Andrew},
	year = {2016},
	pages = {57--72}
}

An in-depth introduction is given in the book

Pitts, Andrew M. 2013. Nominal Sets: Names and Symmetry in Computer Science. Cambridge University Press. https://doi.org/10.1017/CBO9781139084673. pdf

@book{pitts_2013,
	title = {Nominal {Sets}: {Names} and {Symmetry} in {Computer} {Science}},
	publisher = {Cambridge University Press},
	author = {Pitts, Andrew M.},
	year = {2013},
	doi = {10.1017/CBO9781139084673},
}

A survey of nominal techniques in set-theoretic language is given in

Gabbay, Murdoch J. 2011. ‘Foundations of Nominal Techniques: Logic and Semantics of Variables in Abstract Syntax’. The Bulletin of Symbolic Logic 17 (2): 161–229. https://doi.org/10.2178/bsl/1305810911. pdf

@article{gabbay_2011,
	title = {Foundations of {Nominal} {Techniques}: {Logic} and {Semantics} of {Variables} in {Abstract} {Syntax}},
	volume = {17},
	doi = {10.2178/bsl/1305810911},
	number = {2},
	journal = {The Bulletin of Symbolic Logic},
	author = {Gabbay, Murdoch J.},
	year = {2011},
	pages = {161--229},
}