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algebra ALGOL 68 analysis argument schema arithmetic assume assumptions axioms calculus Carnap causal cell classical co-model coherence conditions computability predicate concept consider consistent constructive contains corresponding countable deduction defined definition denote diophantine equations elementary submodel elements empirical equivalent example existential exists finite formal formula genetics given Godel number hence hypothesis inductive inference rules integers intermediate logics interpretation intuitionistic intuitionistic logic kind language lattice Lemma logical space mathematical means Mendelian method microtheory modal logic Moschovakis natural numbers notion objects observation obtained operation parameters Philosophy of Science physical polynomial possible Prawitz Prewellordering principles probability problem programming proof theory propensity propositional proved quantum mechanics question reason recursive function relation satisfies scientific Section semantics sense sentences sequence solution specific properties statistical strongly valid structure theorem tion true Turing machine University valid with respect values variables