There exist two definitions of consistency: semantical and syntactical.

Semantical definition uses the notion of a model and says:

a set is consistent if it has a model.

Syntactical definition uses the notion of provability and says:

a set is consistent if one can’t prove a contradiction from it.

— Cse371, Math371, LOGIC, Fall 2011

— Professor Anita Wasilewska

2012.09.12 Wednesday ACHK