Perturbative and constructive arguments show that the Gross-Neveu mode
l with N greater than or equal to 2 flavor degrees is asymptotically f
ree. Assuming canonical anticommutation relations (CAR), which are qui
te plausible, and some technicalities, we show for the Thirring model,
i.e., the case of N = 1 flavor, that the fields are necessarily free.
This explains from an axiomatic point of view the different behavior
depending on the number of flavors. (C) 1996 American Institute of Phy
sics.