Assuming w is the only measurable cardinal, we prove: Let ˜ be an equivalence relation such that ˜ = =l for some logic L < L* satisfying Robinson’s consistency theorem (with L* arbitrary); then there exists a strongest logic L+ < L* such that ˜ = =l+; in addition, L+ is countably compact if. Let ˜ be an equivalence relation such that ˜ = =tp for some logic L° satisfying Robinson’s consistency theorem and whose sentences of any type r are (up to equivalence) equinumerous with some cardinal kt; then L° is the unique logic L such that ˜ = =l\ furthermore, L° is compact and obeys Craig’s interpolation theorem. We finally give an algebraic characterization of those equivalence relations ˜ which are equal to =l for some compact logic L obeying Craig’s interpolation theorem and whose sentences are equinumerous with some cardinal.

Duality between logics and equivalence relations / D. MUNDICI. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - STAMPA. - 270:(1982), pp. 111-129. [10.2307/1999763]

Duality between logics and equivalence relations

MUNDICI, DANIELE
1982

Abstract

Assuming w is the only measurable cardinal, we prove: Let ˜ be an equivalence relation such that ˜ = =l for some logic L < L* satisfying Robinson’s consistency theorem (with L* arbitrary); then there exists a strongest logic L+ < L* such that ˜ = =l+; in addition, L+ is countably compact if. Let ˜ be an equivalence relation such that ˜ = =tp for some logic L° satisfying Robinson’s consistency theorem and whose sentences of any type r are (up to equivalence) equinumerous with some cardinal kt; then L° is the unique logic L such that ˜ = =l\ furthermore, L° is compact and obeys Craig’s interpolation theorem. We finally give an algebraic characterization of those equivalence relations ˜ which are equal to =l for some compact logic L obeying Craig’s interpolation theorem and whose sentences are equinumerous with some cardinal.
1982
270
111
129
D. MUNDICI
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/311459
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