## Notre Dame Journal of Formal Logic

### Complexity of the -query Tautologies in the Presence of a Generic Oracle

Toshio Suzuki

#### Abstract

Extending techniques of Dowd and those of Poizat, we study computational complexity of in the case when is a generic oracle, where is a positive integer, and denotes the collection of all -query tautologies with respect to an oracle . We introduce the notion of ceiling-generic oracles, as a generalization of Dowd's notion of -generic oracles to arbitrary finitely testable arithmetical predicates. We study how existence of ceiling-generic oracles affects behavior of a generic oracle, by which we show that is not a subset of is comeager in the Cantor space. Moreover, using ceiling-generic oracles, we present an alternative proof of the fact (Dowd) that the class of all -generic oracles has Lebesgue measure zero.

#### Article information

Source
Notre Dame J. Formal Logic Volume 41, Number 2 (2000), 142-151.

Dates
First available in Project Euclid: 25 November 2002

https://projecteuclid.org/euclid.ndjfl/1038234608

Digital Object Identifier
doi:10.1305/ndjfl/1038234608

Mathematical Reviews number (MathSciNet)
MR1932226

Zentralblatt MATH identifier
1015.03045

#### Citation

Suzuki, Toshio. Complexity of the -query Tautologies in the Presence of a Generic Oracle. Notre Dame J. Formal Logic 41 (2000), no. 2, 142--151. doi:10.1305/ndjfl/1038234608. https://projecteuclid.org/euclid.ndjfl/1038234608

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