Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The rst attempt at a systematic approach to axiomatic theories of truth was undertaken by Friedman and Sheard [11]. There tlve principles consisting of axioms, axiom schemata and rules of inference, each embodying a reasonable property of truth re isolated for study. Working with a base theory of truth conservative over PA, Friedman and Sheard raised the following questions. Which subsets of the Optional Axioms are consistent over the base theory? What are the proof-theoretic strengths of the consistent theories? The rst question was ansred completely by Friedman and Sheard; all subsets of the Optional Axioms re classied as either consistent or inconsistent giving rise to nine maximal consistent theories of truth. They also determined the proof-theoretic strength of two subsets of the Optional Axioms. The aim of this paper is to continue the work begun by Friedman and Sheard.  will establish the proof-theoretic strength of all the remaining seven theories and relate their arithmetic part to llknown theories ranging from PA to the theory of 1 dependent choice.
['Graham E. Leigh', 'Michael Rathjen']
I am writing a research paper on a idea An ordinal analysis for theories of self-referential truth
[{"from": "human", "value": "I am writing a research paper on a idea An ordinal analysis for theories of self-referential truth"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The rst attempt at a systematic approach to axiomatic theories of truth was undertaken by Friedman and Sheard [11]. There tlve principles consisting of axioms, axiom schemata and rules of inference, each embodying a reasonable property of truth re isolated for study. Working with a base theory of truth conservative over PA, Friedman and Sheard raised the following questions. Which subsets of the Optional Axioms are consistent over the base theory? What are the proof-theoretic strengths of the consistent theories? The rst question was ansred completely by Friedman and Sheard; all subsets of the Optional Axioms re classied as either consistent or inconsistent giving rise to nine maximal consistent theories of truth. They also determined the proof-theoretic strength of two subsets of the Optional Axioms. The aim of this paper is to continue the work begun by Friedman and Sheard.  will establish the proof-theoretic strength of all the remaining seven theories and relate their arithmetic part to llknown theories ranging from PA to the theory of 1 dependent choice."}]