# Blocking the Routes to Triviality with Depth Relevance

## Abstract

In Rogerson and Restall’s (J Philos Log 36, 2006, p. 435), the “class of implication formulas known to trivialize (NC)” (NC abbreviates “naïve comprehension”) is recorded. The aim of this paper is to show how to invalidate any member in this class by using “weak relevant model structures”. Weak relevant model structures verify deep relevant logics only.

## Keywords

Naive set theory Weak relevant model structures Depth relevance Deep relevant logics## Notes

### Acknowledgments

Work supported by research project FFI2011-28494 financed by the Spanish Ministry of Economy and Competitiveness. G. Robles is supported by Program Ramón y Cajal of the Spanish Ministry of Economy and Competitiveness. We sincerely thank a referee of the Journal of Logic, Language and Information for his/her comments and suggestions on a previous draft of this paper.

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