Abstract

We prove a combinatorial result for models of the 4-fragment of the Simple Theory of Types , TST4. The result says that if is a standard transitive and rich model of TST4, then satisfies the 0,0,n-property, for all n≥2. This property has arisen in the context of the consistency problem of the theory New Foundations . The result is a weak form of the combinatorial condition that was shown in Tzouvaras [5] to be equivalent to the consistency of NF. Such weak versions were introduced in Tzouvaras [6] in order to relax the intractability of the original condition. The result strengthens one of the main theorems of Tzouvaras [5, Theorem 3.6] which is just equivalent to the 0,0,2-property