Geodesic
Nice infinitary logics
Shelah, Saharon1, 2
1 Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel
2 Department of Mathematics, Hill Center - Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019
Journal of the American Mathematical Society, Tome 25 (2012) no. 2, pp. 395-427

Voir la notice de l'article provenant de la source American Mathematical Society

We deal with soft model theory of infinitary logics. We find a logic between $\mathbb {L}_{\infty ,\aleph _0}$ and $\mathbb {L}_{\infty ,\infty }$ which has some striking properties. First, it has interpolations (it was known that each of those logics fails interpolation though the pair has interpolation). Second, well ordering is not characterized in a strong way. Third, it can be characterized as the maximal such nice logic (in fact, it is the maximal logic stronger than $\mathbb {L}_{\infty ,\aleph _0}$ and which satisfies “well ordering is not characterized in a strong way”).
DOI : 10.1090/S0894-0347-2011-00712-1

Shelah, Saharon 1, 2

1 Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel
2 Department of Mathematics, Hill Center - Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019 
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Shelah, Saharon. Nice infinitary logics. Journal of the American Mathematical Society, Tome 25 (2012) no. 2, pp. 395-427. doi: 10.1090/S0894-0347-2011-00712-1

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