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Learning, Realizability and Games in Classical Arithmetic
[article]
2011
arXiv
pre-print
In this dissertation we provide mathematical evidence that the concept of learning can be used to give a new and intuitive computational semantics of classical proofs in various fragments of Predicative Arithmetic. First, we extend Kreisel modified realizability to a classical fragment of first order Arithmetic, Heyting Arithmetic plus EM1 (Excluded middle axiom restricted to Sigma^0_1 formulas). We introduce a new realizability semantics we call "Interactive Learning-Based Realizability". Our
arXiv:1012.4992v5
fatcat:4iksfoith5b6zjarfihdtosr3e