FOM:infinity

[Fernando Ferreira]

Joe Shipman:
"By the way, are there any nice finitely axiomatizable systems which 
stand in the same relation to Peano Arithmetic or to Finite Set 
Theory as Godel-Bernays set theory stands to ZFC? (that is, they may 
introduce new predicates but are conservative extensions with respect 
to sentences which don't use the new predicates)."

ACA_0 is a well-known conservative extension of PA, and it is 
finitely axiomatizable. It has two sorts of variables, but it can be 
reformulated with only one sort of variables (at the cost of 
introducing new predicates).

Fernando Ferreira
CMAF - Universidade de Lisboa
Av. Professor Gama Pinto, 2
P-1649-003 Lisboa
PORTUGAL
ferferr at cii.fc.ul.pt
http://alf1.cii.fc.ul.pt/~ferferr/
tel: (351)-217904893