countable choice axiom computable examples - SERP Analysis

https://en.wikipedia.org/wiki/Axiom_of_countable_choice

https://mathoverflow.net/questions/23246/peculiar-examples-with-axiom-of-countable-choice

https://math.stackexchange.com/questions/721503/the-axiom-of-countable-choice

https://proofassistants.stackexchange.com/questions/1011/is-there-computational-interpretation-for-countable-choice

https://ncatlab.org/nlab/show/countable%2Bchoice

https://www.infinitelymore.xyz/p/axiom-of-choice

https://www.i-programmer.info/programming/theory/6156-axiom-of-choice-the-programmers-guide-.html?start=1

https://en.wikipedia.org/wiki/Axiom_of_choice

https://www.quora.com/Whats-the-difference-between-the-countable-principle-of-choice-and-the-axiom-of-dependent-choices

https://www.math.utoronto.ca/ivan/mat327/docs/notes/11-choice.pdf

https://www.reddit.com/r/math/comments/76ea3f/measure_theory_and_the_axiom_of_choice/

https://gowers.wordpress.com/2008/08/10/a-small-countability-question/

https://arxiv.org/abs/2412.08667

https://proofwiki.org/wiki/Axiom:Axiom_of_Countable_Choice

https://sites.dartmouth.edu/dujs/2010/03/24/equivalents-of-a-failure-of-the-axiom-of-choice/

https://ncatlab.org/nlab/show/axiom%2Bof%2Bchoice

https://www.reddit.com/r/math/comments/14d6w7/how_to_explain_axiom_of_choice_to_people_who_dont/

https://news.ycombinator.com/item?id=13571315

https://www.jstor.org/stable/2586854

https://planetmath.org/axiomofcountablechoice

https://www.youtube.com/watch?v=AviisQCpMP4

https://shelah.logic.at/files/95685/E51.pdf

https://www.sciencedirect.com/science/article/pii/S0168007220300129

https://web.sas.upenn.edu/jinwei/files/2025/03/Pizza_Talk_2024.pdf

https://www.parabola.unsw.edu.au/sites/default/files/2024-02/vol58_no3_6.pdf

https://rocq-prover.org/doc/v8.17/stdlib/Coq.Logic.ChoiceFacts.html

https://plato.stanford.edu/entries/reverse-mathematics/

http://adam.chlipala.net/cpdt/html/Cpdt.Universes.html

https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-33/issue-2/The-axiom-of-choice-for-countable-collections-of-countable-sets/10.1305/ndjfl/1093636102.pdf

https://graphsearch.epfl.ch/concept/421086

https://proofwiki.org/wiki/Axiom_of_Dependent_Choice_Implies_Axiom_of_Countable_Choice

https://cameroncounts.wordpress.com/tag/axiom-of-choice/

https://philpapers.org/browse/the-axiom-of-choice

https://inria.hal.science/hal-02088293v1/document

https://pi.math.cornell.edu/~shore/papers/pdf/RMComp7.pdf

https://www.irif.fr/~krivine/articles/GeoCal04.pdf

https://karagila.org/tags/axiom-of-choice/

https://arxiv.org/pdf/2006.01614

https://lmcs.episciences.org/7478/pdf

https://coq.inria.fr/doc/v8.9/stdlib/Coq.Logic.ChoiceFacts.html

https://digitalworks.union.edu/cgi/viewcontent.cgi?article=1045&context=theses

https://builds.openlogicproject.org/content/set-theory/choice/countablechoice.pdf

https://math.ucr.edu/~res/math144/setsnotes7.pdf

https://www.physicsforums.com/threads/is-axiom-of-choice-applicationless.254602/

http://settheory.net/model-theory/infinity-choice

https://jdh.hamkins.org/tag/axiom-of-determinacy/

https://golem.ph.utexas.edu/category/2024/11/axiomatic_set_theory_9_the_axi.html

https://www.cs.virginia.edu/~robins/Turing_Paper_1936.pdf

https://people.math.wisc.edu/~awmille1/old/m873-08/ac.pdf

https://jaydaigle.net/blog/more-on-the-axiom-of-choice/

https://www.researchgate.net/publication/321152932_On_fixed-point_theorems_in_synthetic_computability

https://math.andrej.com/asset/data/synthetic.pdf

https://yforster.de/downloads/talk-pls24.pdf

https://cornellmath.wordpress.com/2007/09/13/the-axiom-of-choice-is-wrong/

https://www.sciencedirect.com/science/article/abs/pii/S0890540121000778

https://lawrencecpaulson.github.io/2021/11/10/Axiom_of_Choice.html

https://news.ycombinator.com/item?id=33775052

https://medium.com/%40zghantiwala7/how-important-is-the-axiom-of-choice-in-mathematics-aa195dcf1d12

https://planetmath.org/variationsonaxiomofchoice

https://link.springer.com/article/10.1007/s00224-023-10118-y

https://math.vanderbilt.edu/schectex/ccc/choice.html

https://www.quora.com/Is-the-axiom-of-countable-choice-enough-to-prove-a-countable-family-of-countable-sets-has-a-countable-union

https://journals.sagepub.com/doi/abs/10.3233/COM-210313

https://drops.dagstuhl.de/storage/00lipics/lipics-vol016-csl2012/LIPIcs.CSL.2012.335/LIPIcs.CSL.2012.335.pdf

https://www.mat.uc.pt/~ggutc/teses/teseingles.pdf

https://www2.math.uconn.edu/~solomon/research/compaut.pdf

https://rjlipton.com/2013/07/30/making-choices/

https://www.irif.fr/~krivine/articles/Edinburgh.pdf

https://terrytao.wordpress.com/2010/03/19/a-computational-perspective-on-set-theory/

http://h.web.umkc.edu/halle/PapersForEveryone/UnionsAndAC.pdf

https://www.youtube.com/watch?v=WaxiL4IRIYw

https://research-portal.uea.ac.uk/files/179880271/ac_pfa_and_chang.pdf

https://foldoc.org/Axiom%2Bof%2BChoice

https://philpapers.org/rec/GUTOCC

https://math.berkeley.edu/~marks/notes/computability_notes_v1.pdf

https://projecteuclid.org/journals/tbilisi-mathematical-journal/volume-10/issue-3/On-fixed-point-theorems-in-synthetic-computability/10.1515/tmj-2017-0107.pdf

https://people.math.ethz.ch/~halorenz/4students/Algebra/AC.pdf

https://rocq-prover.org/doc/v8.9/stdlib/Coq.Logic.ChoiceFacts.html

https://personal.math.ubc.ca/~PLP/book/section-44.html

https://shelah.logic.at/files/95439/E33.pdf

http://www.ma.huji.ac.il/~ohadfeld/Tsirelson/Courses/MeasCategory/lect4.pdf

https://mathforums.com/t/countable-union-of-countable-sets-question.340015/

https://mathstodon.xyz/%40MartinEscardo/112011057976815731

https://plato.stanford.edu/entries/axiom-choice/

http://blog.rongarret.info/2023/01/an-intutive-counterexample-to-axiom-of.html

https://kuscholarworks.ku.edu/server/api/core/bitstreams/cf6b05fe-617a-4e75-9ee6-f1f4a5107f44/content

http://alexmennen.com/index.php/2021/02/28/cardinality-and-the-axiom-of-choice/

https://math.andrej.com/asset/data/madison-synthetic-computability-talk.pdf

https://cs.uwaterloo.ca/~alopez-o/math-faq/node69.html

https://www.i-programmer.info/babbages-bag/1902-non-computable-numbers.html

http://www.goodmath.org/blog/2014/05/26/you-cant-even-describe-most-numbers/

https://sciencehouse.wordpress.com/2011/09/02/computability/

https://www.researchgate.net/publication/262486989_Axiom_of_Choice

https://billwadge.com/2017/06/12/thanks-axiom-of-choice-the-banachtarski-paradox/

https://risingentropy.com/axiom-of-choice-and-hats/

https://lsa.umich.edu/content/dam/math-assets/math-document/reu-documents/Lauri-Elizabeth.pdf

https://groups.google.com/g/constructivenews/c/PeLsQWDFJNg/m/7piOmUHbAAAJ

https://jaydaigle.net/blog/what-is-the-axiom-of-choice/

https://www.cambridge.org/core/books/all-the-mathematics-you-missed/countability-and-the-axiom-of-choice/D6AD54AE5DCE5744D592167D97707A68