caa a22 4500 469126604 CHVBK 20180323133152.0 cr unu---uuuuu 170328e19921101xx s 000 0 eng 10.1007/BF01277481 doi (NATIONALLICENCE)springer-10.1007/BF01277481 Tiny models of categorical theories [Elektronische Daten] [M. Laskowski, A. Pillay, P. Rothmaler] Summary: We explore the existence and the size of infinite models of categorical theories having cardinality less than the size of the associated Tarski-Lindenbaum algebra. Restricting to totally transcendental, categorical theories we show that "Every tiny model is countable” is independent of ZFC. IfT is trivial there is at most one tiny model, which must be the algebraic closure of the empty set. We give a new proof that there are no tiny models ifT is not totally transcendental and is non-trivial. Springer-Verlag, 1992 Laskowski M. MSRI and University of Maryland, 20742, College Park, MD, USA aut Pillay A. Department of Mathematics, University of Notre Dame, P.O. Box 398, 46556, Notre Dame, IN, USA aut Rothmaler P. Philosophisches Seminar, Abteilung Logik, Christian-Albrechts-Universität zu Kiel, Olshausenstrasse 40-60, W-2300, Kiel, Federal Republic of Germany aut Archive for Mathematical Logic Springer-Verlag 31/6(1992-11-01), 385-396 0933-5846 31:6<385 1992 31 153 https://doi.org/10.1007/BF01277481 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01277481 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Laskowski M. MSRI and University of Maryland, 20742, College Park, MD, USA aut NATIONALLICENCE 700 1- Pillay A. Department of Mathematics, University of Notre Dame, P.O. Box 398, 46556, Notre Dame, IN, USA aut NATIONALLICENCE 700 1- Rothmaler P. Philosophisches Seminar, Abteilung Logik, Christian-Albrechts-Universität zu Kiel, Olshausenstrasse 40-60, W-2300, Kiel, Federal Republic of Germany aut NATIONALLICENCE 773 0- Archive for Mathematical Logic Springer-Verlag 31/6(1992-11-01), 385-396 0933-5846 31:6<385 1992 31 153 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer