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The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program
, 2001
"... . After a brief flirtation with logicism in 19171920, David Hilbert proposed his own program in the foundations of mathematics in 1920 and developed it, in concert with collaborators such as Paul Bernays and Wilhelm Ackermann, throughout the 1920s. The two technical pillars of the project were the ..."
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. After a brief flirtation with logicism in 19171920, David Hilbert proposed his own program in the foundations of mathematics in 1920 and developed it, in concert with collaborators such as Paul Bernays and Wilhelm Ackermann, throughout the 1920s. The two technical pillars of the project were the development of axiomatic systems for ever stronger and more comprehensive areas of mathematics and finitistic proofs of consistency of these systems. Early advances in these areas were made by Hilbert (and Bernays) in a series of lecture courses at the University of Gttingen between 1917 and 1923, and notably in Ackermann 's dissertation of 1924. The main innovation was the invention of the ecalculus, on which Hilbert's axiom systems were based, and the development of the esubstitution method as a basis for consistency proofs. The paper traces the development of the "simultaneous development of logic and mathematics" through the enotation and provides an analysis of Ackermann's consisten...
Skolem functions and Hilbert’s ǫterms in Free Variable Tableau Systems
"... Abstract. We apply the framework of the generic δrule presented in [4] to show how to map the δ ǫrule, which uses ǫterms as syntactical objects to expand existentially quantified formulae, in the context of standard δrules based on Skolem terms. Structural results coming out from such mapping pr ..."
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Abstract. We apply the framework of the generic δrule presented in [4] to show how to map the δ ǫrule, which uses ǫterms as syntactical objects to expand existentially quantified formulae, in the context of standard δrules based on Skolem terms. Structural results coming out from such mapping process are discussed. 1