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Martin Sleziak
Martin Sleziak
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Just to add a couple of references: 1- John Franks' paper titled "Cantor’s Other Proofs that R Is Uncountable" is available at http://www.jstor.org/stable/10.4169/002557010X521822 (unfortunately, not for free) 2- and Akihiro Kanamori & David Pincus' paper titled "Does GCH Imply AC Locally" is available at http://math.bu.edu/people/aki/7.pdf (for free). 3- You might also like looking at "Diagonalizing by Fixed-Points" by "Ahmad Karimi & Saeed Salehi" (available at arxiv.org) where some of the above mentioned proofs have been discussed.

  1. John Franks' paper titled "Cantor’s Other Proofs that R Is Uncountable" is available at https://www.jstor.org/stable/10.4169/002557010X521822 (unfortunately, not for free)
  2. and Akihiro Kanamori & David Pincus' paper titled "Does GCH Imply AC Locally" is available at http://math.bu.edu/people/aki/7.pdf (for free).
  3. You might also like looking at "Diagonalizing by Fixed-Points" by "Ahmad Karimi & Saeed Salehi" (available at arxiv.org) where some of the above mentioned proofs have been discussed.

Just to add a couple of references: 1- John Franks' paper titled "Cantor’s Other Proofs that R Is Uncountable" is available at http://www.jstor.org/stable/10.4169/002557010X521822 (unfortunately, not for free) 2- and Akihiro Kanamori & David Pincus' paper titled "Does GCH Imply AC Locally" is available at http://math.bu.edu/people/aki/7.pdf (for free). 3- You might also like looking at "Diagonalizing by Fixed-Points" by "Ahmad Karimi & Saeed Salehi" (available at arxiv.org) where some of the above mentioned proofs have been discussed.

Just to add a couple of references:

  1. John Franks' paper titled "Cantor’s Other Proofs that R Is Uncountable" is available at https://www.jstor.org/stable/10.4169/002557010X521822 (unfortunately, not for free)
  2. and Akihiro Kanamori & David Pincus' paper titled "Does GCH Imply AC Locally" is available at http://math.bu.edu/people/aki/7.pdf (for free).
  3. You might also like looking at "Diagonalizing by Fixed-Points" by "Ahmad Karimi & Saeed Salehi" (available at arxiv.org) where some of the above mentioned proofs have been discussed.
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Saeed Salehi
Saeed Salehi
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Just to add a couple of references: 1- John Franks' paper titled "Cantor’s Other Proofs that R Is Uncountable" is available at http://www.jstor.org/stable/10.4169/002557010X521822 (unfortunately, not for free) 2- and Akihiro Kanamori & David Pincus' paper titled "Does GCH Imply AC Locally" is available at http://math.bu.edu/people/aki/7.pdf (for free). 3- You might also like looking at "Diagonalizing by Fixed-Points" by "Ahmad Karimi & Saeed Salehi" (available at arxiv.org) where some of the above mentioned proofs have been discussed.