@incollection(buss:1998,
 author       = "Samuel R. Buss",
 year         = "1998",
 title        = "First-Order Proof Theory of Arithmetic",
 booktitle    = "Handbook of Proof Theory",
 chapter      = "II",
 series       = "Studies in Logic and the Foundations of Mathematics",
 volume       = "137",
 publisher    = "Elsevier",
 pages        = "79--147",
)
@book(kleene:1952,
 author       = "Stephen Kleene",
 year         = "1952",
 title        = "Introduction to Metamathematics",
 publisher    = "Wolters-Noordhof, Groningen",
)
@article(leivant:2002,
 author       = "Daniel Leivant",
 year         = "2002",
 title        = "Intrinsic reasoning about functional programs {I}: first order theories",
 journal      = "Annals of Pure and Applied Logic",
 volume       = "114",
 number       = "1--3",
 pages        = "117--153",
 doi          = "10.1016/S0168-0072(01)00078-1",
)
@book(troelstra:2000,
 author       = "Anne Sjerp Troelstra and Helmut Schwichtenberg",
 year         = "2000",
 title        = "Basic proof theory (2nd edition)",
 publisher    = "Cambridge University Press",
 address      = "New York, NY, USA",
)