In recursion theory, hyperarithmetic theory is a generalization of Turing computability. It has close connections with definability in second-order… (More)

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2013

2013

- Barbara F. Csima, Johanna N. Y. Franklin, Richard A. Shore
- Notre Dame Journal of Formal Logic
- 2013

We study arithmetic and hyperarithmetic degrees of categoricity. We extend a result of Fokina, Kalimullin, and R. Miller to show… (More)

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2010

2010

- Steffen Lempp
- 2010

We define a family of properties on hyperhypersimple sets and show that they yield index sets at each level of the… (More)

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2006

2006

A mass problem is a set of Turing oracles. If P and Q are mass problems, we say that P is weakly reducible to Q if for all Y ∈ Q… (More)

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2005

2005

A statement of hyperarithmetic analysis is a sentence of second order arithmetic S such that for every Y ⊆ ω, the minimum ω-model… (More)

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2002

1996

1996

- Ivan N. Soskov
- Math. Log. Q.
- 1996

The main result proved in the paper is that on every recursive structure the intrinsically hyperarithmetical sets coincide with… (More)

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1994

1987

1987

- Christopher J. Ash
- Ann. Pure Appl. Logic
- 1987

We say that a recursive structure 92 is A°-categorical, for cr < ~o cK, if for every recursive structure ~ ~ 92 there exists an… (More)

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1971

1971

- Alan L. Selman
- 1971

Introduction It has been remarked by Addison ([1]) and Hinman ([6]) that applications of forcing techniques (Cohen ([2… (More)

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1970