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Andrés E. Caicedo
Andrés E. Caicedo
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Can all the large cardinal axioms not presently known to be inconsistent with ZFC be arranged in a strict linear order based on the following criterion. Let A(1) and A(2) be any distinct pair of these axioms and let both be adjoined to ZFC. We will say that A(1)<A(2)$A(1)\lt A(2)$ if and only if the smallest cardinal number satisfying A(1) is smaller than the smallest cardinal number satisfying A(2). Should such a strict linear ordering of these axioms be possible, which of them ranks the largest?

Can all the large cardinal axioms not presently known to be inconsistent with ZFC be arranged in a strict linear order based on the following criterion. Let A(1) and A(2) be any distinct pair of these axioms and let both be adjoined to ZFC. We will say that A(1)<A(2) if and only if the smallest cardinal number satisfying A(1) is smaller than the smallest cardinal number satisfying A(2). Should such a strict linear ordering of these axioms be possible, which of them ranks the largest?

Can all the large cardinal axioms not presently known to be inconsistent with ZFC be arranged in a strict linear order based on the following criterion. Let A(1) and A(2) be any distinct pair of these axioms and let both be adjoined to ZFC. We will say that $A(1)\lt A(2)$ if and only if the smallest cardinal number satisfying A(1) is smaller than the smallest cardinal number satisfying A(2). Should such a strict linear ordering of these axioms be possible, which of them ranks the largest?

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Garabed Gulbenkian
Garabed Gulbenkian
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A question about large cardinal axioms.

Can all the large cardinal axioms not presently known to be inconsistent with ZFC be arranged in a strict linear order based on the following criterion. Let A(1) and A(2) be any distinct pair of these axioms and let both be adjoined to ZFC. We will say that A(1)<A(2) if and only if the smallest cardinal number satisfying A(1) is smaller than the smallest cardinal number satisfying A(2). Should such a strict linear ordering of these axioms be possible, which of them ranks the largest?