Special relativity derives from two postulates:
Invariance of $c$
Principle of relativity
The same axiomatic procedure is possible for quantum mechanics. Now, does exist a set of axioms for general relativity in order the derive the theory in a straightforward way? I would say that one of them is the "equivalence principle" and the others?
Einstein's general relativity has no postulates:
https://www.quora.com/What-are-the-postulates-of-General-Relativity What are the postulates of General Relativity? Alexander Poltorak, Adjunct Professor of Physics at the CCNY:
In 2005 I started writing a paper, “The Four Cornerstones of General Relativity on which it doesn’t Rest.” Unfortunately, I never had a chance to finish it. The idea behind that unfinished article was this: there are four principles that are often described as “postulates” of General Relativity:
Principle of general relativity
Principle of general covariance
Equivalence principle
Mach principle
The truth is, however, that General Relativity is not really based on any of these “postulates” although, without a doubt, they played important heuristic roles in the development of the theory.
Sometimes Einsteinians absurdly call the final equations of general relativity "postulates":
http://math.stanford.edu/~schoen/trieste2012/lecture_3.pdf
Postulates of General Relativity Postulate 1: A spacetime (M^4, g) is a Riemannian 4-manifold M^4 with a Lorentzian metric g. Postulate 2: A test mass beginning at rest moves along a timelike geodesic. (Geodesic equation) ... Postulate 3: Einstein equation is satisfied. (Einstein equation) ..."
Special relativity is deductive (even though a false postulate and an invalid argument spoiled it from the very beginning) but general relativity is an empirical model, analogous to the empirical models defined here:
http://collum.chem.cornell.edu/documents/Intro_Curve_Fitting.pdf
The objective of curve fitting is to theoretically describe experimental data with a model (function or equation) and to find the parameters associated with this model. Models of primary importance to us are mechanistic models. Mechanistic models are specifically formulated to provide insight into a chemical, biological, or physical process that is thought to govern the phenomenon under study. Parameters derived from mechanistic models are quantitative estimates of real system properties (rate constants, dissociation constants, catalytic velocities etc.). It is important to distinguish mechanistic models from empirical models that are mathematical functions formulated to fit a particular curve but whose parameters do not necessarily correspond to a biological, chemical or physical property."
