[1]
AvigadJ.,
*Formalizing forcing arguments in subsystems of second-order arithmetic*
. Annals of Pure and Applied Logic, vol. 82 (1996), pp. 165–191.

[2]
BeklemishevL. and VisserA.,
*On the limit existence principles in elementary arithmetic and*
${\rm{\Sigma }}_n^0$
*-consequences of theories*
. Annals of Pure and Applied Logic, vol. 136 (2005), pp. 56–74.

[3]
BlanckR.,
*Two consequences of Kripke’s lemma*
, Idées Fixes (KasåMartin, editor), University of Gothenburg Publications, 2014, pp. 45–53.

[4]
BoolosG., The Logic of Provability, Cambridge University Press, Cambridge, 1979.

[6]
D’AquinoP.,
*A sharpened version of McAloon’s theorem on initial segments of* IΔ_{0}
. Annals of Pure and Applied Logic, vol. 61 (1993), pp. 49–62.

[7]
DimitracopoulosC. and ParisJ.,
*A note on a theorem of H. Friedman*
. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 34 (1988), pp. 13–17.

[8]
DimitracopoulosC. and PaschalisV.,
*End extensions of models of weak arithmetic theories*
. Notre Dame Journal of Formal Logic, to appear.

[9]
EnayatA. and WongT.,
*Model theory of*
${\rm{WKL}}_0^{^{\rm{*}}}$
. Annals of Pure and Applied Logic, to appear.

[10]
GuaspariD.,
*Partially conservative extensions of arithmetic*
. Transaction of the American Mathematical Society, vol. 254 (1979), pp. 47–68.

[11]
HájekP.,
*Interpretability and fragments of arithmetic*
. Arithmetic, Proof Theory, and Computational Complexity, Oxford University Press, Oxford, 1993, pp. 185–196.

[12]
HájekP. and PudlákP., Metamathematics of First-Order Arithmetic, Springer-Verlag, Berlin, 1993.

[13]
JaparidzeG. and de JonghD.,
*The logic of provability*
, Handbook of Proof Theory, North-Holland, Amsterdam, 1998, pp. 475–546.

[14]
KayeR., Models of Peano Arithmetic, Oxford University Press, Oxford, 1991.

[15]
KossakR. and SchmerlJ., The Structure of Models of Peano Arithmetic, Oxford University Press, Oxford, 2006.

[16]
KripkeS.,
*“Flexible” predicates of formal number theory*
. Proceedings of the American Mathematical Society, vol. 13 (1962), pp. 647–650.

[17]
LindströmP., Aspects of Incompleteness, Lecture Notes in Logic, vol. 10, ASL Publications, 1997.

[18]
McAloonK., *On the complexity of models of arithmetic*, this Journal, vol. 47 (1982), pp. 403–415.

[19]
RessayreJ.-P.,
*Nonstandard universes with strong embeddings, and their finite approximations*
, Logic and Combinatorics, Contemporary Mathematics, vol. 65, American Mathematical Society, Providence, RI, 1987, pp. 333–358.

[20]
RogersH., Theory of Recursive Functions and Effective Computability, McGraw-Hill, Cambridge, MA, 1967.

[22]
SimpsonS., Subsystems of Second Order Arithmetic, Springer-Verlag, Berlin, 1999.

[23]
SmoryńskiC., Modal Logic and Self-reference, Springer-Verlag, Berlin, 1985.

[24]
VerbruggeR. and VisserA., A small reflection principle for bounded arithmetic, this Journal, vol. 59 (1994), pp. 785–812.

[25]
WoodinW. H.,
*A potential subtlety concerning the distinction between determinism and nondeterminism*
, Infinity, New Research Frontiers (HellerM. and WoodinW. H., editors), Cambridge University Press, Cambridge, 2011, pp. 119–129.