Special issue of Logica Universalis „Scope of Logic Theorems”. Call for papers, 2011

Scope of Logic Theorems
Special Issue – 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 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 analycity 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 of validity and domain of application of
logic theorems is welcome, in particular those dealing with the following

– Löwenheim-Skolem (1915-1920)
– completeness (Post 1921 – Gödel 1930)
– incompleteness (Gödel 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 mathématiclen, un mathématicien moderne en particulier, se trouve,
dirait-on, à un degré superieur de l’activité consciente: il ne s’intéresse
pas seulement a la question de quoi, mais aussi à celle du comment. Il ne se
borne presque jamais à une solution -tout court- d’un problème, il veut
avoir toujours les solutions les plus … les plus quoi? -les plus faciles,
les plus courtes, les plus générales, etc.”

A.Lindenbaum, „Sur la simplicité formelle des notions”, in Actes du congrès
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


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