Abstract
The intention of the investigations to which the present work belongs is to find an axiomatic basis of the recursion theory for which the following qualities are desirable to possess:(1) to be algebraically styled; that means we expect to find a suitable algebraic language, which is simple and well working and allows us to obtain a connection between recursion theory and same algebraic structures which may be interesting by themselves; (2) to have as large as possible area of applications, i.e. we expect for those structures to have many and easy constructable models: (3) to allow us to prove all the basic facts of the recursion theory in the abstract case, especially the least fixed point or first recursion theorem.
Research partially supported by the Ministry of Culture Science and Education. Contract No 933 1988.
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References
H. P. Barendregt, “The Lambda Calculus. Its Syntax and Semantics”, North-Holland, Amsterdam (1981).
J. A. Zashev, Basic recursion theory in partially ordered models of some fragments of the combinatory logic, C. R.Acad. bulg. Sci., 37:561 (1984).
D. G. Skordev. “Combinatory spaces and recursiveness in them” (Russian), BAN, Sofia (1980).
L. L. Ivanov,. “Algebraic Recursion Theory”, Ellis Horwood, Chichester (1986).
J. A. Zashev, Abstract Plotkin’s models, in: “Mathematical theory of programming”, A. P. Ershov, D.G. Skordev, ed., Novosibirsk (1985).
J. A. Zashev, B-combinatory algebras, Serdica Bulo. math. publ., 12: 225 (1986).
J. A. Zashev. Recursion theory in B-combinatory algebras (Russian), Serdica Bulb. math. publ., 13: 210 (1987).
P. Aczel. An introduction to inductive definitions, in: “Handbook of Mathematical Logic”, J. Barwise, ed., North Holland, Amsterdam (1977).
D. S. Scott, Lectures on a mathematical theory of computation, in: “Theoritical Foundations of Programming Methodology”, M. Broy and G. Schmidt, ed.. D. Reidel Publishing Co, Dordreht (1982).
J. L. Ershov, “Theory of numerations” (Russian). Nauka. Moskow (1977).
J. A. Zashev, “Recursion theory in partially ordered combinatory models” ( Bulgarian ), Thesis. Sofia University (1984).
S. C. Kleene, “Introduction to Metamathematics”. North-Holland, Amsterdam (1952).
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© 1990 Plenum Press, New York
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Zashev, J. (1990). Least Fixed Points in Preassociative Combinatory Algebras. In: Petkov, P.P. (eds) Mathematical Logic. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0609-2_28
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DOI: https://doi.org/10.1007/978-1-4613-0609-2_28
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