A combinatorial result related to the consistency of New Foundations

作者：Tzouvaras Athanassios^*

来源：Annals of Pure and Applied Logic, 2011, 162(5): 373-383.

DOI：10.1016/j.apal.2010.11.003

• Simple Theory of Types
• New Foundations
• Coherent triple of partitions
• Extendibility of coherent triple

We prove a combinatorial result for models of the 4-fragment of the Simple Theory of Types (TST), TST(4). The result says that if A = < A(0), A(1). A(2). A(3)> is a standard transitive and rich model of TST(4), then A 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 (NF). The result is a weak form of the combinatorial condition (existence of omega-extendible coherent triples) that was shown in Tzouvaras (2007) [5] to be equivalent to the consistency of NF. Such weak versions were introduced in Tzouvaras (2009) [6] in order to relax the intractability of the original condition. The result strengthens one of the main theorems of Tzouvaras (2007) [5, Theorem 3.6] which is just equivalent to the < 0, 0, 2 >-property.

• 出版日期2011-3