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Since the definition of the Busy Beaver function by Rado in 1962, an interesting open question has been the smallest value of n for which BB(n) is independent of ZFC set theory.
Gödel, K. “The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis with the Axioms of Set Theory.” Published in 1940 by the Princeton University Press. Annals of Mathematics Studies
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Schoenfield, J. “The Problem of Predicativity.” Essays on the foundations of mathematics, Y. Bar-Hillel et al., eds., pp. 132-142. 1961
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Rado, T. “On Non-Computable Functions.” Bell System Technical Journal, 41: 3. May 1962 pp 877-884
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Lin, S., Rado, T. “Computer Studies of Turing Machine Problems.” Published in Journal of the ACM, Volume 12, Issue 2, April 1965. Pages 196-212
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Brady, A.H. “Solution of the Non-computable ‘Busy Beaver’ game for k = 4 k=4 .” Abstracts for: ACM Computer Science Conference (Washington, DC, February 18-20, 1975), p. 27, ACM, 1975
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Marxen, H., Buntrock, J. “Attacking the Busy Beaver 5.” Bull EATCS, Vol. 40, pp. 247-251. 1990
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Chaitin, G. “The Limits of Mathematics.” pp. 79. 1994
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Koza, J. “Spontaneous Emergence of Self-Replicating and Evolutionarily Self-Improving Computer Programs.” in Artificial Life III (SFI Studies in the Sciences of Complexity, vol. XVII), C. G. Langton, Ed. Reading, MA: Addison-Wesley. pp. 225-262. 1994
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Pargellis, A. “The Spontaneous Generation of Digital ‘Life.”’ Physica D, 91, 86-96. 1996
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Ben-Amram, A., Petersen, H. “Improved Bounds for Functions Related to Busy Beavers” Theory of Computing Systems 35, 1-11 (2002)
2002
Cited alongside, same era.
Calude, C., Calude, E. “Evaluating the Complexity of Mathematical Problems: Part 1,” “Evaluating the Complexity of Mathematical Problems: Part 2.” Complex Systems 18, pp. 387-401. 2010
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Cloudy176, Wythagoras. “A good bound for S(7)?” 2014. http://googology.wikia.com/wiki/User_blog:Wythagoras/A_good_bound_for_S%287%29%3F
2014
Later among the works it cites.
Friedman, H. “Order Invariant Graphs and Finite Incompleteness.” https://u.osu.edu/friedman.8/files/2014/01/FIiniteSeqInc062214a-v9w7q4.pdf
2014
Later among the works it cites.
Friedman, H. “Order Theoretic Equations, Maximality, and Incompleteness.” June 7, 2014. http://u.osu.edu/friedman.8/foundational-adventures/downloadable-manuscripts
2014
Later among the works it cites.
Friedman H. “The Upper Shift Kernel Theorems.” October 9, 2010. https://u.osu.edu/friedman.8/files/2014/01/KernStruThm100910-1lu0b8v.pdf
2014
Later among the works it cites.
Aaronson, S. “The 8000th Busy Beaver number eludes ZF set theory: new paper by Adam Yedidia and me.” May 3, 2016. http://www.scottaaronson.com/blog/?p=2725#comments
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Cited alongside, same era.
Deedlit11, Wythagoras. “Okay, more Turing machines.” 2013. http://googology.wikia.com/wiki/User_blog:Deedlit11/Okay,_more_Turing_machines
2013
Cited alongside, same era.
Barker, C. “Iota and Jot: the Simplest Languages?” http://semarch.linguistics.fas.nyu.edu/barler/Iota/ [A website describing the Iota and Jot programming languages]
Cited in the paper.
Browder, F. “Mathematical Developments Arising from Hilbert Problems.” American Mathematical Society. Volume 28, Part 1
Cited in the paper.
Personal communications with H. Friedman
Cited in the paper.
Madore, D. “The Unlambda Programming Language.” http://www.madore.org/~david/programs/unlambda/
Cited in the paper.
Marxen, H. http://www.drb.insel.de/~heiner/BB/
Cited in the paper.
Müller, U. “Brainfuck.” http://www.muppetlabs.com/~breadbox/bf/
Cited in the paper.
2016
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