AczelPeter, An introduction to inductive definitions, in , pp. 739–782.
AvigadJeremy, Formalizing forcing arguments in subsystems of second-order arithmetic, Annals of Pure and Applied Logic, vol. 82 (1996), pp. 165–191.
On the relationship between ATR0
, Journal of Symbolic Logic, vol. 61 (1996), pp. 768–779.
AvigadJeremy and SommerRichard, The model-theoretic ordinal analysis of theories of predicative strength, Journal of Symbolic Logic, to appear.
BarwiseJon, The handbook of mathematical logic, North-Holland, 1977.
FefermanSolomon, Theories of finite type related to mathematical practice, in , pp. 913–971.
FefermanSolomon, Iterated inductive fixed-point theories: Application to Hancock's conjecture, Patras logic symposium (MetakidesG., editor), North-Holland, 1982.
FriedmanHarvey, Iterated inductive definitions and
-AC, Intuitionism and proof theory (KinoA.
et al., editors), North-Holland, 1970, pp. 435–442.
FriedmanHarvey, McAloonKenneth, and SimpsonStephen, A finite combinatorial principle which is equivalent to the 1-consistency of predicative analysis, Patras logic symposium (MetakidesG., editor), North-Holland, 1982, pp. 197–230.
HájekPetr and PudlákPavel, Metamathematics of first-order arithmetic, Springer-Verlag, 1991.
KayeRichard, Models of Peano arithmetic, Oxford University, 1991.
KetonenJussi and SolovayRobert, Rapidly growing Ramsey functions, Annals of Mathematics, vol. 113 (1981), pp. 267–314.
KirbyL. and ParisJ., Initial segments of models of Peano's axioms, Springer-Verlag Lecture Notes in Mathematics, vol. 619, 1977, pp. 211–216.
KotlarskiH. and RatajczykZ., Inductive full satisfaction classes, Annals of Pure and Applied Logic, vol. 47 (1990), pp. 199–223.
ParisJeff B., A hierarchy of cuts in models of arithmetic, Springer-Verlag Lecture Notes in Mathematics, vol. 834, 1980, pp. 312–337.
ParisJeff B. and HarringtonLeo, A mathematical incompleteness in Peano arithmetic, in , pp. 1132–1142.
PohlersWolfram, Proof theory: An introduction, Springer-Verlag Lecture Notes in Mathematics, vol. 1407, 1989.
PohlersWolfram, A short course in ordinal analysis, Proof theory (Aczel
et al., editors), Cambridge University Press, 1993.
RatatczykZygmunt, Subsystems of true arithmetic and hierarchies of functions, Annals of Pure and Applied Logic, vol. 64 (1993), pp. 95–152.
RathjenMichael, Admissible proof theory and beyond, Logic, methodology, and the philosophy of science IX (PrawitzD.
et al., editors), Elsevier, 1994, pp. 123–147.
RathjenMichael, Proof theory of reflection, Annals of Pure and Applied Logic, vol. 68 (1994), pp. 181–224.
RathjenMichael, Recent advances in ordinal analysis: -CA and related systems, this Bulletin, vol. 1 (1995), pp. 468–485.
RoseH. E., Subrecursion: Functions and hierarchies, Clarendon, 1984.
SchütteKurt, Proof theory, Springer-Verlag, 1977.
SchwichtenbergHelmut, Proof theory: Some applications of cut-elimination, in , pp. 867–895.
SimpsonStephen G., Subsystems of second order arithmetic, preprint.
SimpsonStephen G., Subsystems of Z2 and reverse mathematics, appendix to Gaisi Takeuti, Proof theory, second ed., North-Holland, 1987.
SimpsonStephen G., On the strength of König's duality theorem of countable bipartite graphs, Journal of Symbolic Logic, vol. 59 (1994), pp. 113–123.
SmithRick, The consistency strengths of some finite forms of the Higman and Kruskal theorems, Harvey Friedman's research on the foundations of mathematics (HarringtonLeo
et al., editors), North-Holland, 1985, pp. 119–135.
SommerRichard, Transfinite induction and hierarchies generated by transfinite recursion within Peano arithmetic,
, University of California, Berkeley, 1990.
SommerRichard, Ordinals in bounded arithmetic, Arithmetic, proof theory, and complexity (ClotePeter and KrajičekJan, editors), Oxford University Press, 1992.
SommerRichard, Transfinite induction within Peano arithmetic, Annals of Pure and Applied Logic, vol. 76 (1995), pp. 231–289.
WainerS. S., A classification of the ordinal recursive functions, Archiv für mathematische Logik, vol. 13 (1970), pp. 136–153.