David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Synthese 164 (3):321 - 332 (2008)
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
George Boole (1951). An Investigation of the Laws of Thought,. [New York]Dover Publications.
Alonzo Church (1944). Introduction to Mathematical Logic. London, H. Milford, Oxford University Press.
William Craig (1960). Bases for First-Order Theories and Subtheories. Journal of Symbolic Logic 25 (2):97-142.
Leon Henkin (1950). Completeness in the Theory of Types. Journal of Symbolic Logic 15 (2):81-91.
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