@misc{Lexicon of Arguments, title = {Quotation from: Lexicon of Arguments – Concepts - Ed. Martin Schulz, 29 Mar 2024}, author = {Field,Hartry}, subject = {Loewenheim}, note = {I 131 Löwenheim-Skolem/downward/Field: says that there must be no uncountable models for 1st order consistent theories. Compactness theorem/Löwenheim-Skolem/upward: says that each 1st order space-time theory, according to which there are infinitely many space-time points, will have models, in which the set of the space-time points is mightier than the set of real numbers. Problem: then the representation theorem does not apply. >Representation theorem.}, note = { Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich, Aldershot 1994 }, file = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=244336} url = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=244336} }