Carnap on extremal axioms and categoricity

Georg Schiemer (MCMP/LMU) gives a talk at the MCMP Workshop on Carnap titled "Carnap on extremal axioms and categoricity". Abstract: The talk will investigate Carnap's early contributions to formal semantics in his work on general axiomatics between 1928 and 1936. Inparticular, we give a historically sensitive discussion of Carnap's theoryof extremal axioms from the late 1920s onwards. The main focus is seton the unpublished documents of the projected second part of UntersuchungenzurallgemeinenAxiomatik (RC 081-01-01 to 081-01-33).We present a formal reconstruction of the semantic notions 'formalmodel', 'model structure', und 'submodel' first formulated there. Themain interprctive issue addressed in the talk concerns Carnap's understandingof the relationship between the "completenessof the models"of an axiomatic theory and other metatheoretic notions investigatedby him at the time, most notably that of semantic completeness andcategoricity.