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Herbrand's Fundamental Theorem: The Historical Facts and their Streamlining [article]

Claus-Peter Wirth
2014 arXiv   pre-print
Using Heijenoort's unpublished generalized rules of quantification, we discuss the proof of Herbrand's Fundamental Theorem in the form of Heijenoort's correction of Herbrand's "False Lemma" and present  ...  Although we are mainly concerned with the inner structure of Herbrand's Fundamental Theorem and the questions of its quality and its depth, we also discuss the outer questions of its historical context  ...  This means, for instance, that presentations of Herbrand's Fundamental Theorem via Herbrand disjunctions, such as in [Heijenoort, 1992, pp. 247-249], should be avoided because they are none of the following  ... 
arXiv:1405.6317v2 fatcat:5drkeurl3bhf3ki725ssbhoaji

A Most Interesting, but Revoked Draft for Hilbert and Bernays' "Grundlagen der Mathematik" that never found its way into any publication, and 2 CV of Gisbert Hasenjaeger [article]

Claus-Peter Wirth
2021 arXiv   pre-print
In 1934, in Bernays preface to the 1st edn. of the 1st vol. of Hilbert-Bernays "Grundlagen der Mathematik", a nearly completed draft of the the finally two-volume monograph is mentioned, which had to be  ...  Moreover, we document when Hasenjaeger stayed in Zurich to assist Bernays in the completion of the 2nd edn.  ...  [Wirth,2012]Claus-PeterWirth, 2012.Herbrand's Fundamental Theorem inthe eyes of Jean van Heijenoort. Logica Universalis, 6:485-520. Received Jan. 12, 2012.  ... 
arXiv:1803.01386v4 fatcat:ai5itqzjnzddpnum2shh5johua

Cut as Consequence

Curtis Franks
2010 History and Philosophy of Logic  
Gentzen's conception of logic is compelling in its own right. It is also of historical interest because it allows for a better understanding of the invention of natural deduction and sequent calculi.  ...  ', and (2) the structure of the sequent calculi li and lk allowed Gentzen to conceptualize completeness as a question about the relationships among a system's individual rules (as opposed to the relationship  ...  Acknowledgments The participants in my spring 2009 proof theory seminar at the University of Notre Dame, with their comments and questions, helped me clarify my reading of Gentzen.  ... 
doi:10.1080/01445340.2010.522365 fatcat:dnibzkfrlfapjkdfxfpaj4d2bm