TY - JOUR
T1 - The Hanf number in the strictly stable case
AU - Shelah, Saharon
N1 - Publisher Copyright:
© 2020 Wiley-VCH GmbH
PY - 2020/10/1
Y1 - 2020/10/1
N2 - We associate Hanf numbers (Formula presented.) to triples (Formula presented.) where T and T1 are theories and p is a type. We show that the Hanf number for the property: “there is a model M1 of (Formula presented.) which omits p, but (Formula presented.) is saturated” is larger than the Hanf number of (Formula presented.) but smaller than the Hanf number of (Formula presented.) when T is stable with (Formula presented.). In fact, surprisingly, we even characterise the Hanf number of (Formula presented.) when we fix (Formula presented.) where T is a first order complete (and stable), (Formula presented.) and demand (Formula presented.).
AB - We associate Hanf numbers (Formula presented.) to triples (Formula presented.) where T and T1 are theories and p is a type. We show that the Hanf number for the property: “there is a model M1 of (Formula presented.) which omits p, but (Formula presented.) is saturated” is larger than the Hanf number of (Formula presented.) but smaller than the Hanf number of (Formula presented.) when T is stable with (Formula presented.). In fact, surprisingly, we even characterise the Hanf number of (Formula presented.) when we fix (Formula presented.) where T is a first order complete (and stable), (Formula presented.) and demand (Formula presented.).
UR - http://www.scopus.com/inward/record.url?scp=85091681287&partnerID=8YFLogxK
U2 - 10.1002/malq.201900021
DO - 10.1002/malq.201900021
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AN - SCOPUS:85091681287
SN - 0942-5616
VL - 66
SP - 280
EP - 294
JO - Mathematical Logic Quarterly
JF - Mathematical Logic Quarterly
IS - 3
ER -