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- Chris J. Conidis
- J. Symb. Log.
- 2008

In 2004 Csima, Hirschfeldt, Knight, and Soare [1] showed that a set A ≤T 0′ is nonlow2 if and only if A is prime bounding, i.e. for every complete atomic decidable theory T , there is a prime model M computable in A. The authors presented nine seemingly unrelated predicates of a set A, and showed that they are equivalent for ∆2 sets. Some of these… (More)

- Chris J. Conidis
- J. Symb. Log.
- 2012

Recently, the Dimension Problem for effective Hausdorff dimension was solved by J. Miller in [Mil], where the author constructs a Turing degree of non-integral Hausdorff dimension. In this article we settle the Dimension Problem for effective packing dimension by constructing a real of strictly positive effective packing dimension that does not compute a… (More)

- Chris J. Conidis
- Theor. Comput. Sci.
- 2012

We answer a recent question of Bienvenu, Muchnik, Shen, and Vereshchagin. In particular, we prove an effective version of the standard fact from analysis which says that, for any ε > 0 and any Lebesgue-measurable subset of Cantor space, X ⊆ 2, there is an open set Uε ⊆ 2, Uε ⊇ X, such that μ(Uε) ≤ μ(X) + ε, where μ(Z) denotes the Lebesgue measure of Z ⊆ 2.… (More)

- Chris J. Conidis, Theodore A. Slaman
- J. Symb. Log.
- 2013

We investigate the question “To what extent can random reals be used as a tool to establish number theoretic facts?” Let 2-RAN be the principle that for every real X there is a real R which is 2-random relative to X . In Section 2, we observe that the arguments of Csima and Mileti [3] can be implemented in the base theory RCA0 and so RCA0 +2-RAN implies the… (More)

- Chris J. Conidis, Richard A. Shore
- IJAC
- 2014

We analyze the complexity of ascendant sequences in locally nilpotent groups, showing that if G is a computable locally nilpotent group and x0; x1; : : : ; xN 2 G, N 2 N, then one can always
nd a uniformly computably enumerable (i.e. uniformly 1) ascendant sequence of order type ! + 1 of subgroups in G beginning with hx0; x1; : : : ; xN iG, the subgroup… (More)

- Chris J. Conidis
- 2009

This article expands upon the recent work by Downey, Lempp, and Mileti [3], who classified the complexity of the nilradical and Jacobson radical of commutative rings in terms of the arithmetical hierarchy. Let R be a computable (not necessarily commutative) ring with identity. Then it follows from the definitions that the prime radical of R is Π1, and the… (More)

- Chris J. Conidis
- Ann. Pure Appl. Logic
- 2010

We prove that if S is an ω-model of weak weak König’s lemma and A ∈ S, A ⊆ ω, is incomputable, then there exists B ∈ S, B ⊆ ω, such that A and B are Turing incomparable. This extends a recent result of Kučera and Slaman who proved that if S0 is a Scott set (i.e. an ω-model of weak König’s lemma) and A ∈ S0, A ⊆ ω, is incomputable, then there exists B ∈ S0,… (More)

- Chris J. Conidis
- 2007

We construct a Π1-class X that has classical packing dimension 0 and effective packing dimension 1. This implies that, unlike in the case of effective Hausdorff dimension, there is no natural correspondence principle (as defined by Lutz) for effective packing dimension. We also examine the relationship between upper box dimension and packing dimension for… (More)

- Chris J. Conidis
- 2008

We construct a Π1-class X that has classical packing dimension 0 and effective packing dimension 1. This implies that, unlike in the case of effective Hausdorff dimension, there is no natural correspondence principle (as defined by Lutz) for effective packing dimension. We also examine the relationship between upper box dimension and packing dimension for… (More)

- Chris J. Conidis, Noam Greenberg, Daniel Turetsky
- Notre Dame Journal of Formal Logic
- 2013

We show that the fact that the first player (“white”) wins every instance of Galvin’s “racing pawns” game (for countable trees) is equivalent to arithmetic transfinite recursion. Along the way we analyse the satisfaction relation for infinitary formulas, of “internal” hyperarithmetic comprehension, and of the law of excluded middle for such formulas.