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Conference Papers Year : 2021

Some Axioms for Mathematics


The λΠ-calculus modulo theory is a logical framework in which many logical systems can be expressed as theories. We present such a theory, the theory $\mathcal{U}$, where proofs of several logical systems can be expressed. Moreover, we identify a sub-theory of $\mathcal{U}$ corresponding to each of these systems, and prove that, when a proof in $\mathcal{U}$ uses only symbols of a sub-theory, then it is a proof in that sub-theory.
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hal-03279749 , version 1 (06-07-2021)



Frédéric Blanqui, Gilles Dowek, Émilie Grienenberger, Gabriel Hondet, François Thiré. Some Axioms for Mathematics. FSCD 2021 - 6th International Conference on Formal Structures for Computation and Deduction, Jul 2021, Buenos Aires / Virtual, Argentina. ⟨10.4230/LIPIcs.FSCD.2021.20⟩. ⟨hal-03279749⟩
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