COARSE REDUCIBILITY AND ALGORITHMIC RANDOMNESS DENIS R. HIRSCHFELDT, CARL G. JOCKUSCH, JR., RUTGER KUYPER, AND PAUL E. SCHUPP Abstract. A coarse description of a set A ⊆ ω is a set D ⊆ ω

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ON NOTIONS OF COMPUTABILITY THEORETIC REDUCTION BETWEEN Π12 PRINCIPLES DENIS R. HIRSCHFELDT AND CARL G. JOCKUSCH, JR. Abstract. Several notions of computability theoretic reducibility between Π12 principles have been s

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ASYMPTOTIC DENSITY AND THE COARSE COMPUTABILITY BOUND DENIS R. HIRSCHFELDT, CARL G. JOCKUSCH, JR., TIMOTHY H. MCNICHOLL, AND PAUL E. SCHUPP Abstract. For r ∈ [0, 1] we say that a set A ⊆ ω is coarsely computable at

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ASYMPTOTIC DENSITY, COMPUTABLE TRACEABILITY, AND 1-RANDOMNESS URI ANDREWS, MINGZHONG CAI, DAVID DIAMONDSTONE, CARL JOCKUSCH, AND STEFFEN LEMPP Abstract. Let r be a real number in the unit interval [0, 1]. A set A ⊆ ω

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Π01 CLASSES AND STRONG DEGREE SPECTRA OF RELATIONS JOHN CHISHOLM, JENNIFER CHUBB, VALENTINA S. HARIZANOV, DENIS R. HIRSCHFELDT, CARL G. JOCKUSCH, JR., TIMOTHY MCNICHOLL, AND SARAH PINGREY Abstract. We study the weak tru

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• Mathematics
• Computer science
• Turing reduction
• Low
• Computable function
• Turing degree
• Function
• Recursive set
• Enumeration
• Computability theory
• Theoretical computer science
• Theory of computation

RESTRICTED JUMP INTERPOLATION IN THE D.C.E. DEGREES Carl G. Jockusch, Jr. and Angsheng Li∗ July 29, 2009

Source URL: www.math.uiuc.edu

• Spectral theory
• Constructible universe
• Turing degree
• Operator theory
• Ordinary differential equations
• Orbifold
• Holomorphic functional calculus
• Mathematics
• Mathematical analysis
• Theoretical computer science

A JOIN THEOREM FOR THE COMPUTABLY ENUMERABLE DEGREES CARL G. JOCKUSCH, JR., ANGSHENG LI, AND YUE YANG Abstract. It is shown that for any computably enumerable (c.e.) degree w, if w 6= 0, then there is a c.e. degree a suc

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• Proof theory
• Limit set
• Mathematics
• Ordinal arithmetic
• Constructible universe
• Mathematical logic
• Ordinal numbers

GENERIC COMPUTABILITY, TURING DEGREES, AND ASYMPTOTIC DENSITY CARL G. JOCKUSCH, JR. AND PAUL E. SCHUPP Abstract. Generic decidability has been extensively studied in group theory, and we now study it in the context of cl

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• Mathematics
• Computer science
• Computable function
• Recursive set
• Computation in the limit
• Generic-case complexity
• Turing reduction
• Halting problem
• Blum axioms
• Computability theory
• Theoretical computer science
• Theory of computation

ASYMPTOTIC DENSITY AND COMPUTABLY ENUMERABLE SETS RODNEY G. DOWNEY, CARL G. JOCKUSCH, JR., AND PAUL E. SCHUPP Abstract. We study connections between classical asymptotic density, computability and computable enumerabilit

Source URL: www.math.uiuc.edu

• Mathematics
• Computer science
• Computable function
• Recursive set
• Recursively enumerable set
• Enumeration
• Generic-case complexity
• Halting problem
• Low
• Computability theory
• Theory of computation
• Theoretical computer science

ASYMPTOTIC DENSITY AND THE ERSHOV HIERARCHY ROD DOWNEY, CARL JOCKUSCH, TIMOTHY H. MCNICHOLL, AND PAUL SCHUPP Abstract. We classify the asymptotic densities of the ∆02 sets according to their level in the Ershov hierarc

Source URL: www.math.uiuc.edu

• Field theory
• Computable number
• Real closed field
• Natural density
• Recursively enumerable set
• Limit superior and limit inferior
• Itō diffusion
• Mathematics
• Theory of computation
• Computability theory