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Minor fixes on grammar
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solatia
solatia
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Recently Toshiyasu Arai submitted "An ordinal analysis of $\Pi_{N}$-Collection" and Henry Towsner submitted "Proofs that Modify Proofs", both of which claimsclaim ordinal analysis of full second-order arithmetic. There has been discussion before on MO about this, see:

The consensus seemed to be that we were a long way away from proving anything like this. For such a big result, I am struggling to find much information on it. I think the two most obvious questions for a lay-person is:

  1. What is claimed to be proof-theoretic ordinal of $Z_2$?
  2. What does this mean for the ordinal analysis of $ZFC$?

Additionally what are the wider implications Proof Theory and Reverse Mathematics?

Recently Toshiyasu Arai submitted "An ordinal analysis of $\Pi_{N}$-Collection" and Henry Towsner submitted "Proofs that Modify Proofs", both of which claims ordinal analysis of full second-order arithmetic. There has been discussion before on MO about this, see:

The consensus seemed to be that we were a long way away from proving anything like this. For such a big result, I am struggling to find much information on it. I think the two most obvious questions for a lay-person is:

  1. What is claimed to be proof-theoretic ordinal of $Z_2$?
  2. What does this mean for the ordinal analysis of $ZFC$?

Additionally what are the wider implications Proof Theory and Reverse Mathematics?

Recently Toshiyasu Arai submitted "An ordinal analysis of $\Pi_{N}$-Collection" and Henry Towsner submitted "Proofs that Modify Proofs", both of which claim ordinal analysis of full second-order arithmetic. There has been discussion before on MO about this, see:

The consensus seemed to be that we were a long way away from proving anything like this. For such a big result, I am struggling to find much information on it. I think the two most obvious questions for a lay-person is:

  1. What is claimed to be proof-theoretic ordinal of $Z_2$?
  2. What does this mean for the ordinal analysis of $ZFC$?

Additionally what are the wider implications Proof Theory and Reverse Mathematics?

Modified question to extend to Towsner's claim
Source Link
solatia
solatia
  • 161
  • 2

Consequences of Toshiyasu Arai'srecent claims of Ordinal Analysis of $Z_2$

Recently Toshiyasu Arai submitted "An ordinal analysis of $\Pi_{N}$-Collection" and Henry Towsner submitted "Proofs that Modify Proofs", both of which claims ordinal analysis of full second-order arithmetic. There has been discussion before on MO about this, see:

The consensus seemed to be that we were a long way away from proving anything like this. For such a big result, I am struggling to find much information on it. I think the two most obvious questions for a lay-person is:

  1. What does Arai claimis claimed to be proof-theoretic ordinal of $Z_2$?
  2. What does this mean for the ordinal analysis of $ZFC$?

Additionally what are the wider implications Proof Theory and Reverse Mathematics?

Consequences of Toshiyasu Arai's Ordinal Analysis of $Z_2$

Recently Toshiyasu Arai submitted "An ordinal analysis of $\Pi_{N}$-Collection", which claims ordinal analysis of full second-order arithmetic. There has been discussion before on MO about this, see:

The consensus seemed to be that we were a long way away from proving anything like this. For such a big result, I am struggling to find much information on it. I think the two most obvious questions for a lay-person is:

  1. What does Arai claim to be proof-theoretic ordinal of $Z_2$?
  2. What does this mean for the ordinal analysis of $ZFC$?

Additionally what are the wider implications Proof Theory and Reverse Mathematics?

Consequences of recent claims of Ordinal Analysis of $Z_2$

Recently Toshiyasu Arai submitted "An ordinal analysis of $\Pi_{N}$-Collection" and Henry Towsner submitted "Proofs that Modify Proofs", both of which claims ordinal analysis of full second-order arithmetic. There has been discussion before on MO about this, see:

The consensus seemed to be that we were a long way away from proving anything like this. For such a big result, I am struggling to find much information on it. I think the two most obvious questions for a lay-person is:

  1. What is claimed to be proof-theoretic ordinal of $Z_2$?
  2. What does this mean for the ordinal analysis of $ZFC$?

Additionally what are the wider implications Proof Theory and Reverse Mathematics?

Source Link
solatia
solatia
  • 161
  • 2

Consequences of Toshiyasu Arai's Ordinal Analysis of $Z_2$

Recently Toshiyasu Arai submitted "An ordinal analysis of $\Pi_{N}$-Collection", which claims ordinal analysis of full second-order arithmetic. There has been discussion before on MO about this, see:

The consensus seemed to be that we were a long way away from proving anything like this. For such a big result, I am struggling to find much information on it. I think the two most obvious questions for a lay-person is:

  1. What does Arai claim to be proof-theoretic ordinal of $Z_2$?
  2. What does this mean for the ordinal analysis of $ZFC$?

Additionally what are the wider implications Proof Theory and Reverse Mathematics?