HumanitiesMathematicsPhilosophyLogicNumber TheoryPhilosophy Of MathematicsIntuitionistic LogicMathematical LogicPhilosophy Of NumberConstructibility Theory
The present note introduces a constructible interpretation for the logical connectives of number theory which is divergent from that of the intuitionists. Under the intuitionistic interpretation, the principle of excluded middle and certain other classically acceptable principles of logic must be rejected. Under the present interpretation, while some classical principles may be reinstated, other principles, acceptable both classically and intuitionistically, may be shown to be invalid. Among these is the principle of contradiction.
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On notation for ordinal numbers
S. C. Kleene · Journal of Symbolic Logic · 1938 · 762 citations
General recursive functions of natural numbers
S. C. Kleene · Mathematische Annalen · 1936 · 595 citations
On the interpretation of intuitionistic number theory
S. C. Kleene · Journal of Symbolic Logic · 1945 · 540 citations
Recursive predicates and quantifiers
S. C. Kleene · Transactions of the American Mathematical Society · 1943 · 341 citations · Full text