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An undecidable problem in the algebra of truth-tables

Published online by Cambridge University Press:  12 March 2014

Jan Kalicki
Jan Kalicki*
Affiliation:
University of California, Berkeley
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Extract

In a previous paper I have described a decision method for testing whether or not two arbitrary finite truth-tables are “equal”, i.e., determine the same set of tautologies. The same problem for the case of infinite truth-tables remained open.

In the present note we shall show that the answer to the problem in the case of infinite truth-tables is negative; in fact we shall prove that there exists neither a decision method for testing the equality of arbitrary truth-tables, nor even one for testing the equality of what we call “recursive” truth-tables.

The terminology of Kalicki [3] will be used; for brevity's sake the discussion involving the notions of recursiveness and recursive enumerability uses the informal terminology and mode of argumentation employed by Post in [9].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 19 , Issue 3 , September 1954 , pp. 172 - 176
Copyright
Copyright © Association for Symbolic Logic 1954

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References

BIBLIOGRAPHY

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