For axiomatic theories, does algorithm exist that can determine if formula is true or false {decision problem}? Do algorithms exist that can determine if formulas with no variables are true or false? Does showing that formula is true or false require formal proof?
In axiomatic theories that contain number theory, it is impossible to decide whether formula is true by any method except formal proof {Church's thesis, truth} {Church thesis, truth}.
3-Mathematics-Axiomatic Theory
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Date Modified: 2022.0225