Abstract
In graph models of combinatory algebras we can represent algebraic, relational, and algorithmic structures as inner algebras (cf. contributions of Engeler, Weibel, and Amrhein). Problems of the original domain are thus transferred into the combinatory algebra and transformed into equations. In this way, the solvability of these problems is reformulated as solvability questions for the corresponding equations. If there is no solution of an equation in a certain inner algebra, we might be able to extend this algebra with an abstract solution. This view of problem solving suggests the application of the paradigm of Galois theory to combinatory algebras.
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References
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© 1995 Birkhäuser Boston
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Gloor, O. (1995). Remarks on an Algebraic Theory of Recursive Degrees. In: The Combinatory Programme. Progress in Theoretical Computer Science. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4268-0_4
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DOI: https://doi.org/10.1007/978-1-4612-4268-0_4
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