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AISB opportunities Bulletin Item

CALL FOR PAPERS: Special issue on "Scope of Logic Theorems"


Special issue of "Logica Universalis": in Memoriam A.Lindenbaum (1904-1941)

In view of the speedy and huge expansion of the universe of logics, the question of the scope of 
validity and the domain of application of fundamental logic theorems is more than ever crucial. 
What is true for classical logic and theories based on it, does not necessarily hold for 
non-classical logics.

But we may wonder if there is a logic deserving the name in which a theorem such as the 
incompleteness theorem does not hold. On the other hand a theorem such as cut-elimination 
does not hold for many interesting logical systems. Cut-elimination expresses the intrinsic 
analicity of a logic, the fact that a proof of a theorem depends only of its constituents, 
a not always welcome feature. Anyway, it is interesting to find necessary and/or sufficient 
conditions for cut-elimination to hold. And also for any important theorem of logic.

Any paper dealing with the scope and validity of logic theorems is welcome, in particular those 
dealing with the following theorems:

- Lwenheim-Skolem (1915-1920)
- completeness (Post 1921 - Gdel 1930)
- incompleteness (Gdel 1931)
- cut-elimination (Gentzen 1934)
- undefinability (Tarski 1936)
- undecidability (Church-Turing, 1936)
- Lindenbaum's extension lemma (1937)
- compactness (Malcev 1938)
- incompleteness for modal logic (Dugundji 1940)
- Beth's definability theorem (1953)
- Craig's interpolation theorem (1957)
- completeness for modal logic (Kripke 1959)
- independence of CH (Cohen 1963)

"Un mathmaticlen, un mathmaticien moderne en particulier, se trouve, dirait-on,  un degr 
superieur de l'activit consciente: il ne s'intresse pas seulement a la question de quoi, mais 
aussi  celle du comment. Il ne se borne presque jamais  une solution -tout court- d'un problme,
il veut avoir toujours les solutions les plus ... les plus quoi? -les plus faciles, les plus 
courtes, les plus gnrales, etc."

A.Lindenbaum, "Sur la simplicit formelle des notions", in Actes du congrs international de 
philosophie scientifiqe, vol. VII, Logique, Hermann, Paris, 1936, pp.28-38.

The issue will include a paper by Jan Wolenski about the life and work of Lindenbaum.