[
Alexander, S. A. 2019a. Intelligence via ultrafilters: structural properties of some intelligence comparators of deterministic Legg-Hutter agents. Journal of Artificial General Intelligence 10(1):24–45.10.2478/jagi-2019-0003
]Search in Google Scholar
[
Alexander, S. A. 2019b. Measuring the intelligence of an idealized mechanical knowing agent. In CIFMA.10.1007/978-3-030-57506-9_13
]Search in Google Scholar
[
Alexander, S. A. 2020a. AGI and the Knight-Darwin Law: why idealized AGI reproduction requires collaboration. In ICAGI.10.1007/978-3-030-52152-3_1
]Search in Google Scholar
[
Alexander, S. A. 2020b. The Archimedean trap: Why traditional reinforcement learning will probably not yield AGI. Journal of Artificial General Intelligence 11(1):70–85.10.2478/jagi-2020-0004
]Search in Google Scholar
[
Bostrom, N. 2003. Ethical issues in advanced artificial intelligence. In Schneider, S., ed., Science fiction and philosophy: from time travel to superintelligence. John Wiley and Sons. 277–284.
]Search in Google Scholar
[
Chaitin, G. 2011. Metaphysics, Metamathematics and Metabiology. In Hector, Z., ed., Randomness through computation. World Scientific.10.1142/9789814327756_0006
]Search in Google Scholar
[
Conway, J. H. 2000. On Numbers and Games. CRC Press, 2nd edition.10.1201/9781439864159
]Search in Google Scholar
[
Ehrlich, P. 2012. The absolute arithmetic continuum and the unification of all numbers great and small. Bulletin of Symbolic Logic 18:1–45.10.2178/bsl/1327328438
]Search in Google Scholar
[
Girard, J.-Y. 1981.
∏21
\prod\nolimits_2^1 {}
-logic, Part 1: Dilators. Annals of Mathematical Logic 21(2-3):75–219.
]Search in Google Scholar
[
Goldblatt, R. 2012. Lectures on the hyperreals: an introduction to nonstandard analysis. Springer.
]Search in Google Scholar
[
Good, I. J. 1969. Gödel’s theorem is a red herring. The British Journal for the Philosophy of Science 19(4):357–358.10.1093/bjps/19.4.357
]Search in Google Scholar
[
Hardy, G. H. 1904. A theorem concerning the infinite cardinal numbers. Quarterly Journal of Mathematics 35:87–94.
]Search in Google Scholar
[
Hibbard, B. 2008. Adversarial sequence prediction. In ICAGI, 399–403.
]Search in Google Scholar
[
Hibbard, B. 2011. Measuring agent intelligence via hierarchies of environments. In ICAGI, 303–308.
]Search in Google Scholar
[
Hrbacek, K., and Katz, M. G. 2020. Infinitesimal analysis without the axiom of choice. Preprint.10.1016/j.apal.2021.102959
]Search in Google Scholar
[
Hutter, M. 2004. Universal artificial intelligence: Sequential decisions based on algorithmic probability. Springer.
]Search in Google Scholar
[
Kirman, A. P., and Sondermann, D. 1972. Arrow’s theorem, many agents, and invisible dictators. Journal of Economic Theory 5(2):267–277.10.1016/0022-0531(72)90106-8
]Search in Google Scholar
[
Knuth, D. E. 1974. Surreal numbers: a mathematical novelette. Addison-Wesley.
]Search in Google Scholar
[
Knuth, D. E. 1976. Big Omicron and big Omega and big Theta. ACM Sigact News 8(2):18–24.10.1145/1008328.1008329
]Search in Google Scholar
[
Legg, S. 2006. Is there an elegant universal theory of prediction? In International Conference on Algorithmic Learning Theory, 274–287. Springer.10.1007/11894841_23
]Search in Google Scholar
[
Liu, S.-C. 1960. An enumeration of the primitive recursive functions without repetition. Tohoku Mathematical Journal 12(3):400–402.10.2748/tmj/1178244403
]Search in Google Scholar
[
Robinson, A. 1974. Non-standard analysis. Princeton University Press.
]Search in Google Scholar
[
Wainer, S., and Buchholz, W. 1987. Provably computable functions and the fast growing hierarchy. In Simpson, S. G., ed., Logic and Combinatorics. AMS.10.1090/conm/065/891248
]Search in Google Scholar
[
Wainer, S. 1989. Slow growing versus fast growing. The Journal of Symbolic Logic 54(2):608–614.10.2307/2274873
]Search in Google Scholar
[
Wang, P. 2019. On Defining Artificial Intelligence. Journal of Artificial General Intelligence 10(2):1–37.10.2478/jagi-2019-0002
]Search in Google Scholar
[
Weiermann, A. 1997. Sometimes slow growing is fast growing. Annals of Pure and Applied Logic 90(1-3):91–99.10.1016/S0168-0072(97)00033-X
]Search in Google Scholar
[
Weiermann, A. 2002. Slow versus fast growing. Synthese 133:13–29.10.1023/A:1020899506400
]Search in Google Scholar
[
Yampolskiy, R. V. 2012. AI-complete, AI-hard, or AI-easy–classification of problems in AI. In The 23rd Midwest Artificial Intelligence and Cognitive Science Conference.10.5402/2012/271878
]Search in Google Scholar
[
Yampolskiy, R. V. 2013. Turing test as a defining feature of AI-completeness. In Artificial intelligence, evolutionary computing and metaheuristics. Springer. 3–17.
]Search in Google Scholar
[
Yampolskiy, R. V. 2020. On Controllability of Artificial Intelligence. Technical report.
]Search in Google Scholar
