Switch to: References

Add citations

You must login to add citations.
  1. Kurt gödel’s first steps in logic: Formal proofs in arithmetic and set theory through a system of natural deduction.Jan von Plato - 2018 - Bulletin of Symbolic Logic 24 (3):319-335.
    What seem to be Kurt Gödel’s first notes on logic, an exercise notebook of 84 pages, contains formal proofs in higher-order arithmetic and set theory. The choice of these topics is clearly suggested by their inclusion in Hilbert and Ackermann’s logic book of 1928, the Grundzüge der theoretischen Logik. Such proofs are notoriously hard to construct within axiomatic logic. Gödel takes without further ado into use a linear system of natural deduction for the full language of higher-order logic, with formal (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Combinatorial analysis of proofs in projective and affine geometry.Jan von Plato - 2010 - Annals of Pure and Applied Logic 162 (2):144-161.
    The axioms of projective and affine plane geometry are turned into rules of proof by which formal derivations are constructed. The rules act only on atomic formulas. It is shown that proof search for the derivability of atomic cases from atomic assumptions by these rules terminates . This decision method is based on the central result of the combinatorial analysis of derivations by the geometric rules: The geometric objects that occur in derivations by the rules can be restricted to those (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • Generality and existence: Quantificational logic in historical perspective.Jan von Plato - 2014 - Bulletin of Symbolic Logic 20 (4):417-448.
    Frege explained the notion of generality by stating that each its instance is a fact, and added only later the crucial observation that a generality can be inferred from an arbitrary instance. The reception of Frege’s quantifiers was a fifty-year struggle over a conceptual priority: truth or provability. With the former as the basic notion, generality had to be faced as an infinite collection of facts, whereas with the latter, generality was based on a uniformity with a finitary sense: the (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
    		•
  • Geometrisation of first-order logic.Roy Dyckhoff & Sara Negri - 2015 - Bulletin of Symbolic Logic 21 (2):123-163.
    That every first-order theory has a coherent conservative extension is regarded by some as obvious, even trivial, and by others as not at all obvious, but instead remarkable and valuable; the result is in any case neither sufficiently well-known nor easily found in the literature. Various approaches to the result are presented and discussed in detail, including one inspired by a problem in the proof theory of intermediate logics that led us to the proof of the present paper. It can (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   15 citations