Do some Bayesians assume that true values of parameters do not exist? A comment in the thread Efficiency of Bayesian Estimator says 

Bayesian doesn't assume that there is a true value

(of a parameter). 
Question: If it is so, could you give a reference to a branch of Bayesians that do not assume existence of true parameter values? And in absence of true values, what are Bayesian parameter estimators supposed to be targeting?
 A: That's not quite true, to abuse a term. But where do we begin? Do we dare ask "quod est veritas?" again? 
A quantum physicist very much believes that the location of an electron exists, it's merely a probabilistic distribution along the valence of an atom. The random variable is the truth, and its characterizations achieved through observation allow us to calculate electrostatic force. 
Particle physics aside, the distinction between a Frequentist and a Bayesian is always, fundamentally the interpretation of probability. 
In Frequentist notation, truth is reflected in statements of probability using a subscript. A corollary is that $P_{H_0}(A \ne a) = 0$ reflects the base assumption that $a$ is the true value of $A$. It is a falsifiable statement.
Interestingly, for the Bayesian, the statement that $P(A \ne a)=0$ is a refusal to allow any further evidence to modify belief, because the likelihood for other evidence will always be multiplied by 0 with such a prior. 
In summary, these two absolute statements of probability are distinguished insofar as for a frequentist truth is the beginning of science and for a Bayesian truth is the end of science. We are always in the middle.
