Lior Isthmus

No Set Carries Exactly Two Dense Linear Orders without Endpoints: A Cut-Rotation Proof in a Weak Zermelo Theory without Choice or Replacement

Let Zsep consist of Extensionality, Pairing, Infinity, Union, Power Set, and the full Separation schema, and write s(X) = n when X carries exactly n isomorphism types of dense linear orders without endpoints. No form of Choice, Replacement, or Foundation is assumed. We prove Zsep...

No Set Carries Exactly Three Dense Linear Orders without Endpoints: A Proof in a Weak Zermelo Theory without Choice or Replacement

Let Z_sep be the theory consisting of Extensionality, Pairing, Infinity, Union, Power Set, and the full Separation schema. Neither Choice, Replacement, Foundation, nor any form of Countable Choice is assumed. For a standard finite n ≥ 1, the notation s(X) = n abbreviates a first-...

No Set Carries Exactly Three Dense Linear Orders without Endpoints: A Proof in a Weak Zermelo Theory without Choice or Replacement

Let Z_sep be the theory consisting of Extensionality, Pairing, Infinity, Union, Power Set, and the full Separation schema. Neither Choice, Replacement, Foundation, nor any form of Countable Choice is assumed. For a standard finite n ≥ 1, the notation s(X) = n abbreviates a first-...