On the scope of computability and formal axiomatic systems
This survey explores the theoretical scope of effective computation and formal axiomatic systems, emphasizing a constructive perspective based on computable trees and their associated path spaces. No new technical results are presented; rather, the aim is to synthesize established results from computability theory and mathematical logic into a unified framework that clarifies what can be computed in principle, complementing the classical emphasis on undecidability results. It is argued that standard models of computation, such as Turing machines and equivalent formalisms, are computationally…
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