Abstract
A (Formula presented.) -tree is full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full (Formula presented.) -Souslin tree may consistently exist. Shelah gave an affirmative answer of height a strong limit Mahlo cardinal (Formula presented.). Here, it is shown that these trees may consistently exist at small cardinals. Indeed, there can be (Formula presented.) many full (Formula presented.) -trees such that the product of any countably many of them is an (Formula presented.) -Souslin tree.
| Original language | English |
|---|---|
| Article number | e12957 |
| Journal | Journal of the London Mathematical Society |
| Volume | 110 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jul 2024 |
Bibliographical note
Publisher Copyright:Journal of the London Mathematical Society© 2024 The Author(s). The Journal of the London Mathematical Society is copyright © London Mathematical Society.