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References
P.Aczel, Non-well-founded sets, CSLI LN N14, Stanford, 1988.
P.Aczel, Introduction to the theory of inductive definitions, in: Handbook of Math. Logic, J.Barwise ed., North-Holland, Amsterdam, 1977.
J.Barwise, Admissible sets and structures. Berlin, Springer, 1975
G.Jäger. Theories for admissible sets. A unifying approach to proof theory, Studies in Proof Theory, Lecture Notes 2, Bibliopolis, 1986.
S.Feferman, Formal theories for transfinite iterations of generalized inductive definitions and some subsystems of analysis, In: Intuitionism and Proof Theory, eds. A.Kino, et al., Amsterdam, North-Holland, 1970, 303–326.
T.Fernando, A Primitive recursive set theory and AFA: on the logical complexity of the largest bisimulation, Report CS-R9213 ISSN 0169-118XCWI P.O.Box 4079, 1009 AB Amsterdam. The Netherlands.
R.O.Gandy, Set-theoretic functions for elementary syntax, in: Proc. in Pure Math., Vol 13, Part II (1974) 103–126.
Y.Gurevich, Algebras of feasible functions, in: FOCS'83 (1983) 210–214.
Y.Gurevich, Towards logic tailored for computational complexity, in: LNM 1104, Springer, Berlin (1984) 175–216.
Y.Gurevich and S.Shelah, Fixed point extensions of first-order logic, Ann. Pure Appl. Logic 32 (1986) 265–280.
N.Immerman, Relational queries computable in polynomial time, in: 14th. STOC (1982) 147–152; cf. Inform. and Control 68 (1986) 86–104.
R.B. Jensen, The fine structure of the constructible hierarchy, Ann.Math. Logic 4 (1972) 229–308.
A.B.Livchak, Languages of polynomial queries, in: Raschet i optimizacija teplotehnicheskih ob'ektov s pomosh'ju EVM, Sverdlovsk, 1982, 41 (in Russian).
Y.N. Moschovakis, Elementary Induction on Abstract Structures, Amsterdam, North-Holland, 1974.
E.Mendelson Introduction to Mathematical Logic, D. Van Nostrand, Princeton, 1964.
V.Yu.Sazonov, Polynomial computability and recursivity in finite domains. EIK, 16, N7 (1980) 319–323.
V.Yu.Sazonov, Bounded set theory and polynomial computability. Conf. on Applied Logic, Novosibirsk, 1985, 188–191. (In Russian)
V.Yu.Sazonov, Collection principle and existetial quantifier. (In Russian) Vychislitel'nye sistemy 107 (1985) Novosibirsk, 30–39.) (Cf. English translation in AMS Transi. (2) 142 (1989) 1–8.)
V.Yu.Sazonov, Bounded set theory, polynomial computability and Δ-programming, Vychislitel'nye sistemy 122 (1987) Novosibirsk, 110–132 (in Russian). Cf. also LNCS 278 (1987) 391–397 (in English).
V.Yu.Sazonov, Bounded Set Theory and Inductive Definability, Logic Colloquium'90, JSL, 56, Nu.3 (1991) 1141–1142.
V.Yu.Sazonov, Hereditarily-finite sets, data bases and polynomial-time computability, TCS 119 (1993) 187–214, Elsevier.
M.Y.Vardi, The complexity of relational query languages, STOC'82, 137–146.
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Sazonov, V.Y. (1995). A bounded set theory with Anti-Foundation Axiom and inductive definability. In: Pacholski, L., Tiuryn, J. (eds) Computer Science Logic. CSL 1994. Lecture Notes in Computer Science, vol 933. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022280
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DOI: https://doi.org/10.1007/BFb0022280
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