Smullyan, Recursion Theory for Metamathematics (Oxford Univ.
Boolos-style proofs of limitative theorems
Beeson Foundations of Constructive Mathematics Metamathematical Studies, (Springer Verlag, New York, 1985).
Towards a Coherent Theory of Physics and Mathematics: The Theory-Experiment Connection
The mathematical schema theory developed in this paper encompasses all types of schemas used in mathematical logic, metamathematics, and set theory. However, it is necessary to stress that here interaction schemas are our main concern.
Mathematical Models in Schema Theory
The countability result has an interesting metamathematical twist.
Measures and their random reals
His remarkable proof involves metamathematical arguments like forcing method and absoluteness.
A classification of separable Rosenthal compacta and its applications