# The Gabbay–Pitts “nominal” NEW quantifier (fresh-ness) иa.φ(a)

The  mathematical meaning to ‘for a fresh name’ introduced in my thesis, introduced in A new approach to abstract syntax with variable binding and the prominent new quantifier of nominal logic.

If you type this into LaTeX…

\usepackage{graphics} %needed for the NEW quantifier
\newcommand\new[0]{\reflectbox{\ensuremath{\mathsf{N}}}}
%The quantifier itself, a reversed sans-serif N
%(by analogy with the reversed E of exists'
%and the reversed A of forall')
\newcommand\New[1]{\new #1.}
%A macro, as in \New{a}\phi
The $\new$ quantifier


… you get this:

This is not a russian letter! It is a reflected sans-serif roman letter, by analogy with ∀ the reflected A of ‘for all’ and ∃ the reflected E of ‘exists’.

I wish I’d thought of this pun but it’s one of Andrew Pitts’s ideas. When we discovered (invented?) the NEW quantifier, he suggested a backwards N notation, and this impressed me very deeply.
Simple and commonsense can also be brilliant — even in computer science. I made a mental note.