# Wydawnictwa / Czasopisma IMPAN / Bulletin Polish Acad. Sci. Math. / Wszystkie zeszyty

## The consistency of level by level equivalence with $V = {\rm HOD}$, the Ground Axiom, and instances of square and diamond

### Tom 68 / 2020

Bulletin Polish Acad. Sci. Math. 68 (2020), 1-10 MSC: 03E35, 03E55. DOI: 10.4064/ba180529-14-3 Opublikowany online: 3 April 2020

#### Streszczenie

We construct via forcing a model for the level by level equivalence between strong compactness and supercompactness in which both $V = {\rm HOD}$ and the Ground Axiom (GA) are true. In our model, various versions of the combinatorial principles $\square$ and $\diamondsuit$ hold. In the model constructed, there are no restrictions on the class of supercompact cardinals.

#### Autorzy

• Arthur W. ApterDepartment of Mathematics
Baruch College of CUNY
New York, NY 10010, U.S.A.
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