@article {IOPORT.00148415,
    author       = {Kuzichev, Andrei A.},
    title        = {Church-Rosser property for some extensions of $\lambda{}\beta$- reducibility relation.},
    year         = {1991},
    journal      = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
    volume       = {37},
    number       = {6},
    issn         = {0044-3050},
    pages        = {547-559},
    publisher    = {VEB Deutscher Verlag der Wissenschaften, Berlin},
    doi          = {10.1002/malq.19910373306},
    abstract     = {We consider non-standard models of formal arithmetic and add its non- standard elements to the language of lambda calculus as new constants. We also extend the deductive ${\cal A}$-system (of lambda conversion) in a natural way. We extract some derivations (so-called $\omega\sb 1$- derivations) and prove that they form a conservative extension of formal arithmetic. To obtain this result we use the Completeness Theorem and prove the Church-Rosser property for the extensions of lambda calculus.},
    reviewer     = {A.A.Kuzichev},
    identifier   = {00148415},
}