Elimination problems in logic: A brief history

Synthese 164 (3):321 - 332 (2008)
Abstract
A common aim of elimination problems for languages of logic is to express the entire content of a set of formulas of the language, or a certain part of it, in a way that is more elementary or more informative. We want to bring out that as the languages for logic grew in expressive power and, at the same time, our knowledge of their expressive limitations also grew, elimination problems in logic underwent some change. For languages other than that for monadic second-order logic, there remain important open problems.
Keywords Elimination of variables and quantifiers  Boolean equations  Monadic second-order logic  Atomless and atomic Boolean algebras  Cardinality quantifiers  Boole  Schröder  Löwenheim  Skolem  Behmann  Ackermann
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References found in this work BETA
Alonzo Church (1944). Introduction to Mathematical Logic. London, H. Milford, Oxford University Press.
Leon Henkin (1950). Completeness in the Theory of Types. Journal of Symbolic Logic 15 (2):81-91.
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