## Notre Dame Journal of Formal Logic

### Forcing Complexity: Minimum Sizes of Forcing Conditions

Toshio Suzuki

#### Abstract

This note is a continuation of our former paper ''Complexity of the r-query tautologies in the presence of a generic oracle.'' We give a very short direct proof of the nonexistence of t-generic oracles, a result obtained first by Dowd. We also reconstitute a proof of Dowd's result that the class of all r-generic oracles in his sense has Lebesgue measure one.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 42, Number 2 (2001), 117-120.

Dates
First available in Project Euclid: 5 June 2003

https://projecteuclid.org/euclid.ndjfl/1054837938

Digital Object Identifier
doi:10.1305/ndjfl/1054837938

Mathematical Reviews number (MathSciNet)
MR1993395

Zentralblatt MATH identifier
1060.03065

#### Citation

Suzuki, Toshio. Forcing Complexity: Minimum Sizes of Forcing Conditions. Notre Dame J. Formal Logic 42 (2001), no. 2, 117--120. doi:10.1305/ndjfl/1054837938. https://projecteuclid.org/euclid.ndjfl/1054837938

#### References

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• [5] Suzuki, T., Computational Complexity of Boolean Formulas with Query Symbols, Ph.D. thesis, University of Tsukuba, Tsukuba-City, 1999.
• [6] Suzuki, T., "Complexity of the $r$"-query tautologies in the presence of a generic oracle, Notre Dame Journal of Formal Logic, vol. 41 (2000), pp. 142–151.
• [7] Suzuki, T., "Degrees of Dowd-type generic oracles", Information and Computation, vol. 176 (2002), pp. 66–87.