I'm reading notes from commutative algebra by Pete Clark.
In one of the examples of Galois connections he introduces notation $\text{RSpec}(K)$ for the set of all total orders on a field $K$, and gives it a topology coming from identifying such order with a function $K^\times\to \{-1, 1\}$, where value $1$ corresponds to positive and $-1$ to negative elements. Then $\text{RSpec}(K)$ is equipped with subspace topology from $\{-1, 1\}^{K^\times}$ which makes it a compact zero-dimensional space.
My question is, where does the notation $\text{RSpec}(K)$ come from? Pete Clark is an arithmetic geometer, so surely this must be notation analogous to that of spectrum and maximal spectrum of a ring?
Edit: Like Alex Kruckman mentioned in the comments, this seems to be analogy for the spectrum of a commutative ring which is more appropriate for formally real fields in real algebraic geometry. The $\text{R}$ in $\text{RSpec}$ stands for "real".