Consistent and inconsistent forcing axioms

Tananimit, Nutt (2023) Consistent and inconsistent forcing axioms. Doctoral thesis, University of East Anglia.

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This thesis explores the relationship between forcing axioms and square principles. While classical forcing axioms, at the level of ω1, are incompatible with square principles, the situation is different for forcing axioms at ω2; in fact, sufficiently strong generalizations of MAω2 actually imply square principles at ω2. Specifically, we prove that the forcing axiom MA1.5 ℵ2 (stratified) implies the weak square □ω1,ω1 . Using this result, we prove the inconsistency of the forcing axiom MMℵ2(ℵ2-c.c.). Moreover, we also prove that MA1.5 ℵ2 (stratified) implies weak Chang’s Conjecture and the existence of a locally compact scattered (LCS) space of height ω2 and width ω.

Item Type: Thesis (Doctoral)
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Nicola Veasy
Date Deposited: 11 Apr 2024 14:11
Last Modified: 11 Apr 2024 14:11


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