EXPANSIONS OF THE ORDERED ADDITIVE GROUP OF REAL NUMBERS BY TWO DISCRETE SUBGROUPS
Philipp Hieronymi · Journal of Symbolic Logic · 2016
Abstract The theory of (ℝ, <, +, ℤ, ℤa) is decidable ifais quadratic. Ifais the golden ratio, (ℝ, <, +, ℤ, ℤa) defines multiplication bya. The results are established by using the Ostrowski numeration system based on the continued fraction expansion ofato define the above structures in monadic second order logic of one successor. The converse that (ℝ, <, +, ℤ, ℤa) defines monadic second order logic of one successor, will also be established.