All Intermediate Logics with Extra Axioms in One Variable, Except Eight, Are Not Strongly $\omega$-Complete
Fiorentini, Camillo
J. Symbolic Logic, Tome 65 (2000) no. 1, p. 1576-1604 / Harvested from Project Euclid
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In [8] it is proved that all the intermediate logics axiomatizable by formulas in one variable, except four of them, are not strongly complete. We considerably improve this result by showing that all the intermediate logics axiomatizable by formulas in one variable, except eight of them, are not strongly $\omega$-complete. Thus, a definitive classification of such logics with respect to the notions of canonicity, strong completeness, $\omega$-canonicity and strong $\omega$-completeness is given.
Publié le : 2000-12-14
Classification:  $\omega$-Canonicity,  Extensive $\omega$-Canonicity,  Strong $\omega$-Completeness,  03B55 
@article{1183746253,
     author = {Fiorentini, Camillo},
     title = {All Intermediate Logics with Extra Axioms in One Variable, Except Eight, Are Not Strongly $\omega$-Complete},
     journal = {J. Symbolic Logic},
     volume = {65},
     number = {1},
     year = {2000},
     pages = { 1576-1604},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183746253}
}

Fiorentini, Camillo. All Intermediate Logics with Extra Axioms in One Variable, Except Eight, Are Not Strongly $\omega$-Complete. J. Symbolic Logic, Tome 65 (2000) no. 1, pp.  1576-1604. http://gdmltest.u-ga.fr/item/1183746253/