David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Bulletin of Symbolic Logic 13 (2):189-225 (2007)
The Löwenheim-Skolem theorem was published in Skolem's long paper of 1920, with the first section dedicated to the theorem. The second section of the paper contains a proof-theoretical analysis of derivations in lattice theory. The main result, otherwise believed to have been established in the late 1980s, was a polynomial-time decision algorithm for these derivations. Skolem did not develop any notation for the representation of derivations, which makes the proofs of his results hard to follow. Such a formal notation is given here by which these proofs become transparent. A third section of Skolem's paper gives an analysis for derivations in plane projective geometry. To clear a gap in Skolem's result, a new conservativity property is shown for projective geometry, to the effect that a proper use of the axiom that gives the uniqueness of connecting lines and intersection points requires a conclusion with proper cases (logically, a disjunction in a positive part) to be proved. The forgotten parts of Skolem's first paper on the Löwenheim-Skolem theorem are the perhaps earliest combinatorial analyses of formal mathematical proofs, and at least the earliest analyses with profound results
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Jan von Plato (2010). Combinatorial Analysis of Proofs in Projective and Affine Geometry. Annals of Pure and Applied Logic 162 (2):144-161.
Similar books and articles
Ignagio Jane (2001). Reflections on Skolem's Relativity of Set-Theoretical Concepts. Philosophia Mathematica 9 (2):129-153.
George S. Boolos (1970). A Proof of the Löwenheim-Skolem Theorem. Notre Dame Journal of Formal Logic 11 (1):76-78.
Thoralf Skolem (1941). Sur la Porté du Théorème Löwenheim-Skolem. In Selected Works in Logic. Universitetsforlaget 455--82.
Timothy Bays (2000). Reflections on Skolem's Paradox. Dissertation, University of California, Los Angeles
Rami Grossberg (1988). A Downward Löwenheim-Skolem Theorem for Infinitary Theories Which Have the Unsuperstability Property. Journal of Symbolic Logic 53 (1):231-242.
Stephen L. Bloom (1973). Extensions of Gödel's Completeness Theorem and the Löwenheim-Skolem Theorem. Notre Dame Journal of Formal Logic 14 (3):408-410.
Timothy Bays (2009). Skolem's Paradox. In Edward N. Zalta (ed.), Stanford Encyclopedia of Philosophy.
Marek Zawadowski (1983). The Skolem-Löwenheim Theorem in Toposes. Studia Logica 42 (4):461 - 475.
Marek Zawadowski (1985). The Skolem-Löwenheim Theorem in Toposes. II. Studia Logica 44 (1):25 - 38.
Alexander George (1985). Skolem and the Löwenheim-Skolem Theorem: A Case Study of the Philosophical Significance of Mathematical Results. History and Philosophy of Logic 6 (1):75-89.
Added to index2009-02-05
Total downloads207 ( #13,074 of 1,792,869 )
Recent downloads (6 months)74 ( #8,623 of 1,792,869 )
How can I increase my downloads?