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Learning theoretic aspects of mathematics and logic have been studied by many authors. They study how mathematical and logical objects are algorithmically \learned" (inferred) from nite data. Although they study mathematical objects, the objective of the studies is learning. In this paper, a mathematics of which foundation itself is learning theoretic will… (More)

We associate to any game G, in the sense of Set Theory, a variant of it we call bck(G). We show through examples that many relevant non-constructive proofs in Algebra and Combinatorics can be interpreted by recursive winning strategy over some game of the form bck(G). We further support this claim by proving that games of the form bck(G) are a sound and… (More)

The notion of Limit-Computable Mathematics (LCM) will be introduced. LCM is a fragment of classical mathematics in which the law of excluded middle is restricted to 1 0 2-formulas. We can give an accountable computational interpretation to the proofs of LCM. The computational content of LCM-proofs is given by Gold's limiting recur-sive functions, which is… (More)