TY - JOUR
T1 - Positive results in abstract model theory
T2 - a theory of compact logics
AU - Makowsky, J. A.
AU - Shelah, S.
PY - 1983/12
Y1 - 1983/12
N2 - We prove that compactness is equivalent to the amalgamation property, provided the occurrence number of the logic is smaller than the first uncountable measurable cardinal. We also relate compactness to the existence of certain regular ultrafilters related to the logic and develop a general theory of compactness and its consequences. We also prove some combinatorial results of independent interest.
AB - We prove that compactness is equivalent to the amalgamation property, provided the occurrence number of the logic is smaller than the first uncountable measurable cardinal. We also relate compactness to the existence of certain regular ultrafilters related to the logic and develop a general theory of compactness and its consequences. We also prove some combinatorial results of independent interest.
UR - http://www.scopus.com/inward/record.url?scp=48749149667&partnerID=8YFLogxK
U2 - 10.1016/0168-0072(83)90021-0
DO - 10.1016/0168-0072(83)90021-0
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AN - SCOPUS:48749149667
SN - 0168-0072
VL - 25
SP - 263
EP - 299
JO - Annals of Pure and Applied Logic
JF - Annals of Pure and Applied Logic
IS - 3
ER -