Set theory in first-order logic: clauses for Go¨del's axioms
Journal of Automated Reasoning
Automated deduction in von Neumann-Bernays-Go¨del set theory
Journal of Automated Reasoning
Functional back-ends within the lambda-sigma calculus
Proceedings of the first ACM SIGPLAN international conference on Functional programming
Computer Proofs in Gödel’s Class Theory with Equational Definitions for Composite and Cross
Journal of Automated Reasoning
Journal of Automated Reasoning
HOL-λσ: an intentional first-order expression of higher-order logic
Mathematical Structures in Computer Science
A finite first-order presentation of set theory
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
A mechanically verified, sound and complete theorem prover for first order logic
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Annals of Mathematics and Artificial Intelligence
Automating theories in intuitionistic logic
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
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We expose a formalism that allows the expression of any theory with one or more axiom schemes using a finite number of axioms. These axioms have the property of being easily orientable into rewrite rules. This allows us to give finite first-order axiomatizations of arithmetic and real fields theory, and a presentation of arithmetic in deduction modulo that has a finite number of rewrite rules. Overall, this formalization relies on a weak calculus of explicit substitutions to provide a simple and finite framework.