Preservation theorems in linear continuous logic
Seyed‐Mohammad Bagheri, Roghieh Safari · Mathematical logic quarterly · 2014
Linear continuous logic is the fragment of continuous logic obtained by restricting connectives to addition and scalar multiplications. Most results in the full continuous logic have a counterpart in this fragment. In particular a linear form of the compactness theorem holds. We prove this variant and use it to deduce some basic preservation theorems.