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Uniform almost everywhere domination

  • Peter Cholak (a1), Noam Greenberg (a2) and Joseph S. Miller (a3)
Abstract
Abstract

We explore the interaction between Lebesgue measure and dominating functions. We show, via both a priority construction and a forcing construction, that there is a function of incomplete degree that dominates almost all degrees. This answers a question of Dobrinen and Simpson, who showed that such functions are related to the proof-theoretic strength of the regularity of Lebesgue measure for Gδ sets. Our constructions essentially settle the reverse mathematical classification of this principle.

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[I] W. Ackermann , Zum Hilbertschen Aufbau der reellen Zahlen., Mathematische Annalen, vol. 99 (1928), pp. 118133.

[7] Carl G. Jockusch Jr. and Richard A. Shore , Pseudojump operators. I. The r.e. case, Transactions of the American Mathematical Society, vol. 275 (1983), no. 2, pp. 599609.

[8] Carl G. Jockusch Jr. and Robert I. Soare , Degrees of members of classes, Pacific Journal of Mathematics, vol. 40 (1972), pp. 605616.

[9] Carl G. Jockusch Jr. and Robert I. Soare , classes and degrees of theories, Transactions of the American Mathematical Society, vol. 173 (1972), pp. 3356.

[10] Antonín Kučera , Measure, -classes and complete extensions of PA, Recursion theory week (Oberwolfach, 1984), Lecture Notes in Mathematics, vol. 1141, Springer, Berlin, 1985, pp. 245259.

[12] D. A. Martin , Classes of recursively enumerable sets and degrees of unsolvability, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 12 (1966), pp. 295310.

[13] André Nies , Lowness properties and randomness, Advances in Mathematics, vol. 197 (2005), pp. 274305.

[15] Stephen G. Simpson , Subsystems of second order arithmetic, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1999.

[17] C. E. M. Yates , Three theorems on the degrees of recursively enumerable sets, Duke Mathematical Journal, vol. 32 (1965), pp. 461468.

[18] Xiaokang Yu and Stephen G. Simpson , Measure theory and weak König's lemma, Archive for Mathematical Logic, vol. 30 (1990), no. 3, pp. 171180.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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