Abstract
ITP is a combinatorial principle that is a strengthening of the tree property. For an inaccessible cardinal κ, ITP at κ holds if and only if κ is supercompact. And just like the tree property, it can be forced to hold at accessible cardinals. A broad project is obtaining ITP at many cardinals simultaneously. Past a singular cardinal, this requires failure of SCH.We prove that from large cardinals, it is consistent to have failure of SCH at κ together with ITP κ+. Then we bring down the result to κ = ? ω2 .
Original language | American English |
---|---|
Pages (from-to) | 5937-5955 |
Number of pages | 19 |
Journal | Transactions of the American Mathematical Society |
Volume | 373 |
Issue number | 8 |
DOIs | |
State | Published - Aug 2020 |
Externally published | Yes |
Bibliographical note
Funding Information:Received by the editors April 4, 2019, and, in revised form, January 26, 2020. 2010 Mathematics Subject Classification. Primary 03E05, 03E35, 03E55. The first author was partially supported by the National Science Foundation, DMS-1500790. The second author was partially supported by FWF, M 2650 Meitner-Programm. The fourth author was partially supported by the National Science Foundation, DMS-1764029. The fifth author was partially supported by the National Science Foundation, Career-1454945. The sixth author was partially supported by the National Science Foundation, DMS-1700425.
Publisher Copyright:
© 2020 American Mathematical Society. All rights reserved.