Remarks on the structure of tt-degrees based on constructive measure theory

Osvald Demuth

Commentationes Mathematicae Universitatis Carolinae (1988)

  • Volume: 029, Issue: 2, page 233-247
  • ISSN: 0010-2628

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Demuth, Osvald. "Remarks on the structure of tt-degrees based on constructive measure theory." Commentationes Mathematicae Universitatis Carolinae 029.2 (1988): 233-247. <http://eudml.org/doc/17629>.

@article{Demuth1988,
author = {Demuth, Osvald},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {T-reducibility; constructive function of a real variable; B- measurability; arithmetization of Lebesgue measurability of sets of reals; constructive measure theory; recursion theory; tt-reducibility},
language = {eng},
number = {2},
pages = {233-247},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Remarks on the structure of tt-degrees based on constructive measure theory},
url = {http://eudml.org/doc/17629},
volume = {029},
year = {1988},
}

TY - JOUR
AU - Demuth, Osvald
TI - Remarks on the structure of tt-degrees based on constructive measure theory
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1988
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 029
IS - 2
SP - 233
EP - 247
LA - eng
KW - T-reducibility; constructive function of a real variable; B- measurability; arithmetization of Lebesgue measurability of sets of reals; constructive measure theory; recursion theory; tt-reducibility
UR - http://eudml.org/doc/17629
ER -

References

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  1. HALMOS P. R., Measure Theory, London, 1966. (1966) 
  2. KUČERA A., Measure, Π 1 0 classes and complete extensions of PA, Lecture Notes in Math., vol. 1141, Springer-Verlag, Berlin 1985, 245-259. (1985) MR0820784
  3. KURTZ S. A., Notions of weak genericity, J. Symbolic Logic 48 (1983), 764-770. (1983) Zbl0549.03042MR0716638
  4. LERMAN M., Degrees of Unsolvability, Springer-Verlag, Berlin, 1983. (1983) Zbl0542.03023MR0708718
  5. ROGERS H., Jr., Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York, 1967. (1967) Zbl0183.01401MR0224462
  6. SACKS G. E., Degrees of unsolvability, Annals of Mathematics Studies 55, Princeton University Press, Princeton, N.J., 1963. (1963) Zbl0143.25302MR0186554
  7. ŠANIN N. A., Constructive Real Numbers and Function Spaces, Trudy Mat. Inst. Steklov 67 (1962), 15-294; English transl., Transl. Math. Monographs, vol. 21, Amer. Math. Soc., Providence, R.I., 1968. (1962) MR0156786
  8. ZASLAVSKIJ I. D., Some properties of constructive real numbers and constructive functions, Trudy Mat. Inst. Steklov 67 (1962), 385-457; English transl., Amer. Math. Soc. Transl. (2) 57 (1966), 1-84. (1962) Zbl0192.06002MR0153555
  9. DEMUTH O., On Lebesgue integration in constructive analysis, Thesis, Moscow State University, 1964 (Russian). (1964) MR0175778
  10. DEMUTH O., The Lebesgue integral and the concept of function measurability in constructive mathematics, Docent Thesis, Charles University, Prague, 1967 (Russian). (1967) 
  11. DEMUTH O., KUČERA A., Remarks on constructive mathematical analysis, Logic Colloquium '78 (Boffa, van Dalen, McAloon ed.), North-Holland, Amsterdam, 81-129. MR0567667
  12. DEMUTH O., The Lebesgue measurability of sets in constructive mathematics, Comment. Math. Univ. Carolinae 10 (1969), 463-492 (Russian). (1969) MR0259055
  13. DEMUTH O., Constructive analogue of the connection between the Lebesgue measurability of sets and of functions, Comment. Math. Univ. Carolinae 14 (1973), 377-396 (Russian). (1973) MR0328015
  14. DEMUTH O., The constructive analogue of the Denjoy-Young theorem on derived numbers, Comment. Math. Univ. Carolinae 17 (1976), 111-126. (1976) MR0403927
  15. DEMUTH O., A constructive analogue of Garg's theorem on Dini derivatives, Comment. Math. Univ. Carolinae 21 (1980), 457-472 (Russian). (1980) 
  16. DEMUTH O., On some classes of arithmetical real numbers, Comment. Math. Univ. Carolinae 23 (1982), 453-465 (Russian). (1982) Zbl0519.03046MR0677854
  17. DEMUTH O., On Borel types of some classes of arithmetical real numbers, Comment. Math. Univ. Carolinae 23 (1982), 593-606 (Russian). (1982) MR0677866
  18. DEMUTH O., On arithmetical complexity of differentiation in constructive mathematics, Comment. Math. Univ. Carolinae 24 (1983), 301-316 (Russian). (1983) MR0711267
  19. DEMUTH O., On pseudo-differentiability of pseudouniformly continuous constructive functions with respect to functions of the same type, Comment. Math. Univ. Carolinae 24 (1983), 391-406 (Russian). (1983) MR0730135
  20. DEMUTH O., A notion of semigenericity, Comment. Math. Univ. Carolinae 28 (1987), 71-84. (1987) Zbl0645.03040MR0889769
  21. DEMUTH O., KUČERA A., Remarks on 1-genericity, semigenericity and related concepts, Comment. Math. Univ. Carolinae 28 (1987), 85-94. (1987) MR0889770
  22. DEMUTH O., Reducibilities of sets based on constructive functions of a real variable, Comment. Math. Univ. Carolinae 29 (1988), 143-156. (1988) Zbl0646.03038MR0937557

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